It depends on the mound. The ridge-top mounds, like Mound 72 which you can see in the lower-left of this reconstruction, were for burials. These are relatively long, low mounds that come to a point at the top.

The Platform Mounds, such as the gigantic Monks Mound, had various structures built on top of them. Based on historical accounts of similar architecture, these structures could be temples, elite houses, treasuries, armories, mortuaries, council houses, etc.

The last major type of mound at the site are the Conical Mounds. In the linked reconstruction, you can see a conical mound as part of the Twin Mounds halfway between Mound 72 and Monks Mound. They're a bit mysterious. By analogy they seem similar to burial mounds built in earlier times, but they've not been confirmed to have that function at Cahokia yet.