When searching a large game tree (for instance using minimax or alpha-beta pruning) it is often unfeasible to search the entire tree, so the tree is normally only partially searched. This results in the horizon effect where a significant change exists just over the "horizon" (slightly beyond the depth the tree has been searched) meaning that evaluating the partial tree gives a misleading result.
An example of the horizon effect occurs when some negative event is inevitable but postponable, because only a partial game tree has been analysed it will appear to the system that the event can be avoided when in fact this is not the case.
Another example comes from writing an AI to play Bridge. If the computer player has a tough decision to make, it will tend postpone it until the end of the hand, even if that isn't the best play.
In chess, the computer player may be looking ahead 20 moves. If there are subtle flaws in its position that only matter after 40 moves, then the computer player can be beaten.