Question

What causes the global air convection current between the equator and the poles?

Answer 1

Because the Earth is (roughly) spherical the Sun's light is distributed over a wider area towards the poles, so has less heating effect.

Explanation:

A diagram may help here:

This effect causes the equatorial regions to be heated considerably more, in turn heating the air masses above them which rise accordingly. The air cools and falls over the poles and returns to the equator closer to the ground.

This assumes there is no other effect (e.g. wind, low or high pressure regions etc.) so represents the simplest case. The reason these things do exist to confound our nice, simple picture is due to the fact that land and ocean heat up at different rates, mountains etc. force air to flow round or over them and there is the coriolis effect (complex, but understandable.)