An endgame tablebase is a computerized database that contains precalculated exhaustive analysis of a chess endgame position. It is typically used by a computer chess engine during play, or by a human or computer that is retrospectively analysing a game that has already been played.
The tablebase contains the game-theoretical value (win, loss, or draw) of each possible move in each possible position, and how many moves it would take to achieve that result with perfect play. Thus, the tablebase acts as an oracle, always providing the optimal moves. Typically the database records each possible position with certain pieces remaining on the board, and the best moves with White to move and with Black to move.
Tablebases are generated by retrograde analysis, working backwards from a checkmated position. Tablebases have solved chess for every position with six or fewer pieces (including the two kings). The solutions have profoundly advanced the chess community's understanding of endgame theory. Some positions which humans had analyzed as draws were proved to be winnable; the tablebase analysis could find a mate in more than a hundred moves, far beyond the horizon of humans, and beyond the capability of a computer during play. Tablebases have enhanced competitive play and facilitated the composition of endgame studies. They provide a powerful analytical tool.
Endgame tablebases for other board games like checkers, chess variants or Nine Men's Morris exist, but without a specific mention of the game, one is talking about chess.