Belt transport system
< Transport network
Items
Technically the only difference between belt types is speed (and colour, of course). In practice, there are some differences in density, throughput and handling in conjunction with inserters. See Transport belts/Physics to dig deeper into that.
Behaviour
Transport belts (conveyor belts) are used to transport Items. They don't need energy to do that, and this is one of the Mysteries of the Factorio World, but like any other mystery in Factorio this is just for gameplay reasons.
The belt transport system can be imagined as "moving ground". Basically every item on a belt is moved in the belts direction.
Technically an item is a small box (turn on the collision box in the Debug mode) and moving means that the position of an item is constantly changed but the items are not allowed to overlap. A picture can show you this better:
Here you can see the items moving upward tick by tick. And when coming to the turn, the items aren't rotated, but moved to the side.
You can see this also very well, when you use the Debug mode and turn on the collision boxes. In this mode you can watch also the collision boxes running on the belt and touching.