Fool’s Mate is a self-mate that is the fastest checkmate in a game of chess. It doesn’t really occur in chess, except perhaps in a real beginner game.
Diagram: Fool’s Mate
There are some similar mates that can occasionally occur. Here’s a trap from the Budapest Opening. After 1. d4 Ng6, 2. Nd2?! e5!?, 3. dxe5 Ng4, 4. h3?? Ne3!! (see diagram). Now White must capture the Knight otherwise lose the trapped Queen, so … 5. fxe3? Qh4+! 6. g3 Qxg3 checkmate.
Diagram: Trap in the Budapest Defence