Simple code is code that's so readable that even novice programmers can work out (at least generally) what the code is doing. (See: Ruby expression syntax)

Impressively complex code is code that does as much as possible in as few lines as possible, without real regard to readability (See: Perl)

Elegant code is code that makes other developers say "Oh man, why didn't I think of that?!" It's sort of in between the first two, with code that may not be so readily apparent that your parents can read it, but not some arcane scrawling that requires a codex to interpret. It does the job, does it well, and doesn't leave the people maintaining the code scratching their heads.