En passant: the rule almost nobody guesses on their own
The most surprising rule in chess, and one of the only ones you can't figure out just by looking at the board.
Key takeaway
An enemy pawn that advances two squares right next to yours can be captured "en passant", but only on your very next move.
"En passant" is the only chess term that stayed in French worldwide, including in official English-language rulebooks. It's the most surprising rule in the game: almost nobody guesses it on their own.
The situation
An enemy pawn, from its starting square, advances two squares in one move (only allowed on its very first move) and ends up right next to one of your pawns, on the same rank. Normally, a pawn only captures diagonally: it shouldn't be able to do anything.
Exception: your pawn is allowed to capture it "en passant", as if it had only advanced one square. Your pawn moves diagonally to the square the enemy pawn would have landed on, and captures it.
The rule to remember
This capture is only available immediately, on the move right after the opponent's two-square push. Play anything else first, even once, and you permanently lose the right for the rest of the game.
It's a right, not an obligation: you're never forced to play it, even when available.
Why this rule exists
The pawn's two-square first move was introduced to speed up the opening. En passant was added in return, so a pawn couldn't safely "jump over" a square an enemy pawn could otherwise have attacked.