There are several ways that a chess match can end in a draw (also called a stalemate).
When a player has no legal move on his / her turn. If it's Black's turn to move in the diagram below, the game ends in a stalemate. Black cannot move the king to any location without putting it in check. Notice the queen covers every square that the Black king can move to, except b7, which the white king could capture. Black's king is not in check, so the position is not checkmate. Instead it is a draw.
When there is insufficient material on the board to checkmate either side. One bishop is not enough to checkmate an opponent. Neither is one knight. Checkmate can be accomplished with a bishop and a knight, or one rook, or one queen. If both sides only have their king and one bishop (or knight), the game is a draw.
When the same position on the board has been seen 3 times.
When 50 moves have gone by with neither team capturing a piece or moving a pawn. The last two stalemate scenarios are rarely seen.