A rule of thumb that usually works and is not guaranteed to. Estimating a journey by distance rather than calculating every route is a heuristic. They are everywhere in practical systems because exact answers are often unaffordable, and they fail in predictable ways at the edges, which is worth knowing before you rely on one.
Technical view
In search, an estimate of the remaining cost to a goal, used to prioritise which branches to explore; admissible heuristics never overestimate and preserve optimality guarantees in algorithms such as A star. More loosely, any approximation adopted for tractability. Much of what looks like intelligence in deployed systems is careful heuristic engineering around a model, and the heuristics are usually where the failures come from.
Related
Part of AI Terminology Index, section: The Foundations.