1. The act of checking a piece of code (or anything else, e.g., a Usenet posting) for completely stupid mistakes. Implies that the check is to make sure the author was sane when it was written; e.g., if a piece of scientific software relied on a particular formula and was giving unexpected results, one might first look at the nesting of parentheses or the coding of the formula, as a sanity check, before looking at the more complex I/O or data structure manipulation routines, much less the algorithm itself. Compare reality check.
2. A run-time test, either validating input or ensuring that the program hasn't screwed up internally (producing an inconsistent value or state).
3. Conversationally, saying “sanity check” means you are requesting a check of your assumptions. “Wait a minute, sanity check, are we talking about the same Kevin here?”