Martinez started the after-school chess club in 1992 after his teacher's lounge rounds of chess with another teacher sparked student interest. His playing partner left the school that year and students began challenging him to matches so the club was born.
Zugzwang, a German chess term mentioned in the movie, is a condition in which a player is forced to move but at a disadvantage. You cannot pass or skip your turn in chess and when you are in zugzwang all available options for you to move have become bad. You are forced to move and are probably going to lose the game. Zugzwang comes up frequently in endgame scenarios where only a few pieces are left on the board.
Based on the true story of Miami Jackson High School chess team's win of the U.S. Chess Federation's National High School Chess Championships in 1998 under the leadership of Cuban-American social studies teacher Mario Martinez (played by Leguizamo).
A draw in chess is a term that comes up in the movie meaning a tie game, neither player wins or loses. In competition both players get half of a point instead of there being a winner with a full point and a loser with no points. Either player can offer to call or claim a draw by mutual agreement and if the other player accepts, the game immediately ends in a tie. Common situations for draws are the threefold repetition, when a player has no other option but to make the same move three times in a row, or draw by stalemate when one player cannot make any further legal moves but their king is not in check.
The Jackson school's chess team is called The Generals.