Heuristics are "rules of thumb".
A heuristic is an attempt at guessing an answer to a problem, which could be correct, but does not guarantee it to be correct (or even suitable).
A common method of applying heuristics is to state the problem, record a number of possible solutions, and then eliminate those which are least likely to be correct.
Continue comparing and eliminating until only one answer is left. That one is probably the closest to being correct.
When dealing with computer viruses, heuristics are used to detect variations of the same infection. For example: One signature can detect "pbot.a", "pbot.c" and "pbot.d", even before the threat is "in the wild".