The original Pokémon game is a trading card game and the theme is "Gota catch them all".
You are right that the Pokémon Go game uses your phones gps, the purpose of the game is to catch as many pokemon as you can. You can battle other pokemon in what is called arenas, these are usually in a public place such as a park. You can set up what I think are called beacons to let people know where pokemon can be found or where arenas are at.
There is probably more to the game but this is the gist of it.