It's Elementary!
Each Pokemon is identified by an element. The element lets you know what kind of characteristics and techniques your Pokemon will have. For example, Water element Pokemon usually live in rivers, lakes, or oceans, and have techniques like Bubble and Hydro Pump.
The element also clues you in to which Pokemon would do well in a battle against another element. Water dampens Fire, and Fire scorches Grass, and Grass covers Water. It is like a more advanced version of rock, paper, scissors.