Heuristic search is a problem solving technique that uses heuristic functions to guide a search through a state space.
It refers to a broad class of algorithms that can be adapted to a variety of problem domains. The most well-known heuristic search technique is probably A* (pronounced "A star").
You may be familiar with its application in games, as it is often used to solve pathfinding problems. For example, when a player clicks on a location for his character to move to, a heuristic search algorithm is often working behind the scenes to find a path.
You can read more on this project's wiki page, artifical intelligence related websites, and in the few books dedicated to the topic.
Free AI Book - Heuristic Search Segment