Some of the promotions give your units a strength bonus, some give your units a bonus against a certain unit type, some make your units better on certain terrain types, while some give your units special abilities such as using enemy roads, faster healing, amphibious attack, and city raider.
Now in Civ4, there are more than 40 promotions you can give to your units as they gain experience, enabling you to customize your units to make them more specialized and more powerful. In previous civ games, units have only a few levels: conscript, regular, veteran, and elite.