Endgame refers to the final part of a chess game, when very few pieces remain on the board. The play was originally written in French, before Beckett translated it back into English himself. The French title, Fin de Partie, can refer to the last segment of a number of different games and not just chess; however, because there's no exact equivalent to the term in English, Beckett went with Endgame.
The point of the title is that, when a chess game reaches the final stages, an advanced player who's going to lose sees that he has been defeated, accepts it, and lets the game play itself out. A novice (beginner), however, will often persist, as if he could get himself out of his situation by stubbornness alone. His moves are trivial, but they still drag out the game. The situation that Clov and Hamm find themselves in at the beginning of the play closely resembles this part of the novice's chess game, and it is only their refusal to accept defeat that prolongs the action of the play.