What is a Game Genre and what are a few?

a game genre is what the game is about and what games may have similar and different each other.
FPS: first person shooter, self-explanatory.
RPG: role-playing game is a game that you play a role in to benefit your team and or progress the story.
MMO: massive multiplayer online, self-explanatory.
TPS: third person shooter, also self explanatory.