This question can be answered at two very different levels: the superficial and the fundamental.
The former, the horserace type of question—i.e., Why did the Jamaicans surge ahead of the Americans  between 2004 and 2008?—is the more interesting one to most people. They want to know which Thoroughbred to bet on in the next race, not why Thoroughbreds are faster than Clydesdales .
In contrast, more fundamental questions about matters that don't change rapidly—e.g., Why have people related to Usain Bolt genealogically, men of West African descent , made up all 56 qualifiers for the finals of the 100 meter dash  in the last seven consecutive Olympics?—are not terribly welcome.
It's not just that the answers tend to imply profoundly unsettling things about humanity . But also … how do you make money off them?
For example, consider the climactic event of the 2008 Olympics, the men's marathon. If it had been won by, say, an African-American named D'Shawn, there would already be literary and movie agents winging their way to Beijing to try to sign him up for an inspiring autobiography, television movie , and motivational speaking tour about how he had "shattered stereotypes " that men of West African descent are better suited for the 100m than the marathon. Stereotype Shattering is big business in the modern world. 
Unfortunately for would-be promoters, the 2008 marathon medals were actually earned by a Kenyan, a Moroccan , and an Ethiopian , boringly reaffirming all the stereotypes about who is best at distance running .
Nobody in America was wowed that a 5'-4" and 112 pound Kenyan  won the marathon. (Actually, it was the first time a Kenyan was victorious in the Olympic marathon. The top Kenyan marathoners, no fools, focus more on the spring and fall marathons, such as the Boston  and New York,  which pay winners in money rather than in medals.)
Yet, it's precisely this ho-hum several-decade-long stability in the racial heritage of the winners of the various men's running events that makes the demographics of running a topic of fundamental interest.
Running is certainly among the most primordial and universal of sports. It's the one about which we can most accurately say: We evolved to do this. We are more likely to be descended from humans who outsprinted charging predators or outjogged wounded prey than from those who did not.
Of course, other sports—whether the pole vault, rhythmic gymnastics, or BMX bike-racing—all make use of evolved skills. But the connection is more indirect. The sports closest in naturalness to track and field (which the rest of the world tellingly calls "athletics ") are the fighting sports—boxing , wrestling , judo and the like. But they are all hedged in with complex rules to keep the competitors from doing too much damage to each other. In contrast, in running, the gun goes off—and the first one across the finish line wins.
This very lack of complexity makes running less than fascinating as a spectator sport —except at the quadrennial Olympics  when the weight of history and the four year wait until the next Olympics bears so heavily on the competitors' shoulders.
Fans who keep up with track and field in-between Summer Games tend to be statistics-loving nerds . This has kept the sport relatively popular in Europe, where the main spectator sport, soccer , was traditionally almost bereft of statistical interest.
Here in the U.S., though, baseball absorbs more of the attention of the numbers-obsessed fraction of the public.
Nonetheless, it's time to think about the fundamentals of running success.
During much of the 20th Century, the backgrounds of the best runners were constantly changing, making it hard to draw inferences about natural talent. The first Olympics were dominated by Chariots of Fire -style English schoolboys and their American cousins. Then emerged Finnish "scientific runners" such as Paavo Nurmi,  followed by long-legged African-American and studious Japanese sprinters , and so forth.
In the last quarter of a century, however, we seem to have reached an equilibrium point. The racial patterns have stabilized. Each distance having its dominant ethnicities.
I've created tables of the 200 fastest times  by racial background for each of the major distances from 100 meters to the marathon (42,000 meters). My calculations aren't perfect, but I spent a lot of time looking at pictures of runners to ascertain their race. For example, the great Cuban 400m and 800m gold medalist at the 1972 and 1976 Games, Alberto Juantorena , wore his hair in the 'fro style popular at the time. These days, however, the balding Juantorena looks quite white .
The results are most informative. For example, here is a graph showing performances by West African runners and their black cousins in the New World.
Blacks of West African descent utterly dominate the 100 meter dash, accounting for all but one of the 200 quickest marks in history. They're almost as dominant at 200m, not quite as overwhelming at 400m, and only modestly competitive at 800m. They aren't world class at any longer lengths, although a black Brazilian did once run a fast marathon in the 1990s.  (Brazilian blacks appear to average more East African ancestry than American and West Indian blacks.)
In contrast, this graph shows the strengths of the three African distance running powerhouses. The Kenyans (green line) are not competitive in the short sprints but occasionally show up in the 400. They are tremendously strong from 800m through the marathon.
The Kenyans' northern neighbors, the Ethiopians (red line), don't emerge until 3000 meters (I've averaged the 3000m steeplechase and the 3000m flat race). They peak at 5000 and 10000 meters.
The northwest Africans (from Morocco, Algeria, and Tunisia) aren't competitive below 800m. Their most famous runners specialized in the 1500 but they are competitive at all the longer distances.
Both the black-skinned Kenyan and brown-skinned Ethiopian runners come overwhelmingly from highland portions of their countries, where evolving an efficient use of the limited oxygen  is crucial.
Moreover, the "running tribe " of Kenya, the Kalenjin, had a history of cattle rustling on foot, sending young men to steal neighbors' cows and stampede them home. The slower ones got spears in their backs, while the faster ones got multiple wives.
The differences between East Africans and West Africans are often overemphasized . While the former tend to have more aerobic capacity and slow twitch muscle fibers and the latter more musculature and more fast twitch fibers, black Africans tend to share the body structure most efficient for running. As O.J. Simpson,  who once shared a world record in the sprint relay with his USC track teammates, explained in 1977 :
"We are built a little differently, built for speed—skinny calves, long legs, high asses are all characteristics of blacks."
The Northwest Africans, such as 2004 Olympic hero Hicham El-Guerrouj , in contrast, are primarily olive-skinned Caucasians. Many Berbers and Arabs live in the tall Atlas Mountains of the Maghreb, but it's not clear whether their runners are predominantly highlanders. El-Guerrouj, for instance, grew up on the Mediterranean. More research into northwest African runners is needed.
People of European descent (blue line) appear to be about equally strong at all distances, but do relatively best at the lengths where West Africans and East Africans aren't as specialized: 400 to 1500 and again at the marathon.
East Asians are noticeable only in the marathon, although there have been several good-but-not-great Japanese sprinters. In the 100, Japanese have comprised four of the 64 semifinalists over the last four Olympics, and they account for one of the top 200 times  at 200 meters.
It's true that each culture has its peculiar favorite length—Americans in the 400, Kenyans in the 3000m steeplechase, and Maghrebians in the 1500.
Still, hereditary differences are the simplest explanation for why track-crazy countries like Kenya, Ethiopia, and Morocco can't buy a sprinter, while Jamaica can't produce a competitive miler. Runners and coaches always have an incentive to explore longer and shorter distances.
The relationship between amount of effort and amount of success in running is usually assumed to be high, but the relationship is complicated. Sprinting requires less exercise to be world class than just about any other sport. In preparation for winning four gold medals at the 1984 Los Angeles Olympics, Carl Lewis worked out eight hours per week .
Distance running is much harder, of course, but it's not at all clear that white people suddenly got lazy when the East Africans emerged.
Consider who runs cross country in American high schools. I looked up the 185 boys who had recorded the 300 fastest times  in high school cross country running (5000 meters distance) in America in 2006. Here, roughly, are the demographics weighted by number of times in the top 300:
Clearly, the East Africans are wildly over-represented (just as they are on Olympic medal stands), since they must be well under 1% of the US population. They are as common as all other minorities combined!
If you subtract the East Africans out, you get whites at 90%, whereas they make up less than 60% of the teenagers in America today. That's rather interesting for what it might say about willingness to put in enormous amounts of effort. (Cross country requires minimal cost, other than shoes, so it's wide open to the less affluent.)
An anonymous commenter on my blog explained:
"Distance running is mostly a smart kid  sport at the high school level. It doesn't require a lot of hand-eye coordination, but rewards determination and self-discipline and gets you the varsity letter that makes you look well-rounded to college admissions boards.  And for bright kids with mile a minute brains, the repetitive, exhausting nature of distance running helps calm the mind and helps these kids get a little centering in their lives."
Similarly, in the U.S., marathon running is an upscale hobby. It's #27  on the list of Stuff White People Like.  The number of Americans finishing a marathon keeps going up yearly, although the average time of finishers has slowed dramatically as the white population ages.
Nevertheless, running is in decline as a spectator sport in the U.S. outside Oregon.
One problem is that doping—most notably, with steroids: artificial male hormones—was long a more visible problem in track than in, say, baseball. This is in part because running is more one-dimensional of a sport than baseball.
It's also because track cracked down harder on dopers. In September 1988, two athletes heavily juiced on steroids set famous records. At the Seoul Olympics, Ben Johnson  won the 100 meter dash in 9.79 seconds. Stateside, Jose Canseco  became the first baseball player to hit 40 homers and steal 40 bases in one season.
Johnson's medal and record was stripped from him two days later. But baseball didn't get around to drug testing until this decade, after muscleheads like Mark McGwire and Barry Bonds had made a joke of the record book.
Runners continued doping, of course, but a new milestone in punishment was reached recently when sprinter Marion Jones, the American heroine of the 2000 Sydney Games,  was sent to prison for lying to federal agents  about her use of performance-enhancing drugs.
Samuel Johnson observed , "When a man knows he is to be hanged in a fortnight, it concentrates his mind wonderfully." Similarly, the current imprisonment of the celebrated Jones has likely concentrated the minds of American Olympians wonderfully.
And, in answer to the superficial question about why Jamaicans outsprinted Americans in 2008, American fear of getting caught probably accounts more than anything else for the performance of American sprinters in Beijing relative to their West Indian rivals.
The Jamaicans and their even smaller neighbors such as Trinidad and the Bahamas have long been contenders, but seldom gold medalists. The lengthy career of the regal sprinter Merlene Ottey , "the Bronze Queen", epitomizes the regional tradition: she garnered eight Olympic medals, none of them gold.
The Jamaicans argue  that the new American drug testing and sanction system has finally leveled the playing field. Americans counter by asserting that now the Jamaicans are more doped than the Americans.
Nobody knows for sure.
For example, the American sprinter most unlikely to be on steroids, the gazelle-like Allyson Felix , finished second in the 200 meters to a Jamaican lady with arms  twice the diameter of hers.
On the other hand, Usain Bolt , while certainly muscular, doesn't appear to be more massively over-developed in his upper body than his rivals, the way Ben Johnson  suddenly became in the mid-1980s. For contrast, here's a picture from 2004 of the American 200m gold medalist Shawn Crawford. 
Considering how awesome Bolt was last week, it seems plausible to assume that if all performance enhancing drugs vanished tomorrow, Bolt would still be the fastest man on Earth.
Ironically, doping among sprinters appears to be an arms race (or a biceps race) that only marginally changes who wins, at least among men.
Thus, the old East German Communist chemical-industrial complex churned out female record setters by the dozens but couldn't manufacture a world class male sprinter. The benefits of a given amount of steroids are much greater for women than men  because men average vastly higher levels of natural testosterone. Thus, male runners need suspiciously large, Ben Johnson-sized doses to make huge improvements, while women can bulk-up significantly on smaller, less-easily detected amounts.
So, in men's running, doping doesn't much change the big picture.
Let's return to the fundamental question: why Jamaica produces such fast sprinters.
An article in Science by Constance Holden, Peering Under the Hood of Africa's Runners , reviewed the state of the art in scientific research on racial differences in running as of 2004.
In 2006, however, Dr. William Aiken, president of the Jamaica Urological Society, offered in the Jamaica Gleaner  a reductionist theory that has the potential to explain many racial differences beyond sprinting:
"I wish to propose a hypothesis that addresses not only the aspect of Jamaica's raw athletic talent, but also encompasses an explanation of seemingly diverse phenomena as our high incidence of prostate cancer (one study found it to be by far the highest in the world at 304 / 100,000 men / year), our high crime rate  (murder capital of the world status earlier this year), our high road traffic accident and fatality rate, and our alleged high levels of promiscuity.
"What do these seemingly disparate phenomena, characteristic of Jamaican life, have in common? On close examination these phenomena are manifestations of high levels of aggressiveness and drive, high libidos, highly efficient muscles from persons of lean body mass and black ethnicity.
"On closer scrutiny all of these phenomena are either related to high circulating levels of testosterone or alternatively to high levels of responsiveness of testosterone receptors to circulating testosterone. It has already been shown that the testosterone receptors of blacks are different genetically to those of whites and this difference confers increased responsiveness to testosterone."[The athletic prowess of Jamaicans , November 22, 2006]