Makyr is partially correct. A checkpoint is a point in the game that automatically saves. Obviously, when this occurs would vary depending on which game you're playing. If you're playing a game which has certain 'tasks' or 'objectives', then after you complete each 'task' (entering a building, killing an enemy), your progress will automatically be saved. A snapshot has nothing to do with saving the game. Literally, a snapshot means that it takes a picture of your screen. Imagine you see something cool or interesting inside your videogame. If you want to take a picture of it, press the snapshot key. Usually it'll be saved to 'My Pictures' or the game directory.

A checkpoint describes a specific location that you have progressed to at which the game will save your progress. Meaning once you have made it to this "checkpoint", this is where you will restart your next game from. A snap shot is similar in that the system has taken a "picture" of your progress. This allows the game or program to remember where you finished so that you can resume from this same place in time or location with your next game.