Wind is, in general, powered by convection. The ground heats up because the sun shines on it. The top of the atmosphere is generally cooler because heat escapes from it into space in the form of infra-red radiation. (The ground can't radiate into space in this way because of greenhouse gases in the atmosphere, which provide it with a kind of thermal blanket.) Since hot air is more buoyant than cold air, it tends to want to rise, and this results in the formation of convection cells, where hot air rises in some places and cool air comes down in other places.
As the other answers have pointed out, the site you linked to shows only the wind speeds at the surface. There are plumes of hot air rising to the top of the atmosphere, and what you see on the map is the air being sucked into the bottom of the plume. If you could see the whole thing in 3D you would see that air rising and then spreading out again at the top of the atmosphere, and then eventually coming back down again in the high-pressure regions where the surface-level winds are diverging.
Because the Earth rotates, there is also a Coriolis force which makes the air tend to rotate as it gets drawn inward toward the plume. You can see this rotation on the map as well. When the same thing happens with a much greater intensity over the ocean, we call it a hurricane.