The GNU project answers this question directly:
http://www.gnu.org/philosophy/free-software-for-freedom.html
The essential difference, slightly oversimplified, is that Free Software generally requires that, if you modify and/or incorporate it into another body of work, the entire result must also be distributed as Free Software, and you are forbidden to further restrict the ability of any "downstream" users from modifying, using, or redistributing the software with the same rights that were given to you.
Disclaimer: Dammit, Jim, I'm a developer, not a lawyer. Don't construe any terms or comments as "legal advice."