An aspiration window is a heuristic used in pair with alpha-beta pruning in order  to reduce search time for combinatorial games by supplying a window (or range) around an estimated score guess.

Alpha-beta pruning achieves its performance by using cutoffs from its original range. Aspiration windows take advantage of this by supplying a smaller initial window, which increases the amount of cutoffs and therefore efficiency.

However, due to search instability, the score may not always be in the window range. This may lead to a costly re-search that can penalize performance. Despite this, popular engines such as Stockfish still use aspiration windows.

The guess that aspiration windows use is usually supplied by the last iteration of iterative deepening.

See also 
 Principal variation search

References

Game artificial intelligence