The Free On-line Dictionary of Computing (30 December 2018):

alpha/beta pruning

    An optimisation of the minimax
   algorithm for choosing the next move in a two-player game.
   The position after each move is assigned a value.  The larger
   this value, the better the position is for me.  Thus, I will
   choose moves with maximum value and you will choose moves with
   minimum value (for me).

   If it is my move and I have already found one move M with
   value alpha then I am only interested in other moves with
   value greater than alpha.  I now consider another of my
   possible moves, M', to which you could reply with a move with
   value beta.  I know that you would only make a different reply
   if it had a value less than beta.  If beta is already less
   than alpha then M' is definitely worth less than M so I can
   reject it without considering any other replies you might
   make.

   The same reasoning applies when considering my replies to your
   reply.  An alpha cutoff is when your reply gives a lower value
   than the current maximum (alpha) and a beta cutoff is when my
   reply to your reply gives a higher value than the current
   minimum value of your reply (beta).

   In short, if you've found one possible move, you need not
   consider another move which your opponent can force to be
   worse than the first one.

   (1997-05-05)