The fifty-move rule is a rule in chess which states that either player may declare a draw if no pawn has been moved and no piece has been captured within the last 50 moves.
This fairly simply rule has a somewhat contentious history. It was originally stated by Ruy López in his Libro de la invención liberal y arte del juego del Axedrez (1561), and has been questioned ever since, with Pietro Carrera arguing for a 24-move rule and Bourdonnais arguing for a 60-move rule. Eventually it was formally shown that some endgames could require more than 50 moves to play out, and a hundred-move rule was introduced, but later it was shown that some endgames could take over a hundred moves, and so everyone threw up their hands and went back to the fifty-move rule.
Over time, the exact criteria of enacting this rule have also been flexible; in some cases the fifty moves did not start being counted until one of the player requested the count start, while in others it was automatic. Under some rules capturing a piece or moving a pawn reset the count, while under others it did not. Some contests allowed a waiver of the rule if a specific endgame was being used, and it was known that more than 50 moves would be needed. And many games simply did not use the fifty-move rule at all.
The rule exists primarily to keep players from spuriously prolonging games, perhaps in an attempt to wear out their opponent. (A "move" in chess is what would be called a "round" in most games, i.e., one move consists of player A taking a turn and then player B taking a turn.) While human players do not generally plan on taking this long on a game and may well welcome the use of the fifty-move rule, it has come into the limelight with the event of AI chess. Notably, the recent landmark match between Alpha Zero and Stockfish was called into question because it was not clear that either opponent had the correct statement of the fifty-move rule.