The minimax score is used in the minimax algorithm for two-player zero-sum game. For each move if it is your oppponent's turn you look for the move that minimises your score (maximises theirs) If it is your move you choose the one that maximises your own score. Of course when calculating the board posotion after a move you can use the same method recursively or a heuristic evaluation if the search depth is too great.
to find minimax score of n
find minimax score of each child of n \\
if it is first_players turn
score of n is the maximum of the children's scores \\
if it is opponents_players turn \\
score of n is the minimum of the children's scores
Used in Chap. 11: page 152
Minimax search on a game tree.