1) free as in "gratis" (freeware software) - you can download it for free, install it and use it. And that's all. Usually it's already compiled so you don't have an access to the source code. Sometimes you are forbidden to copy it and give it to a friend (because you both should e.g. download it from author's web page).

2) free as in "freedom" (free software) - you can do literally anything with this kind of software because it's licensed in a way that doesn't restrict the user in any manner (i.e. license preserves user freedom). Run it, fork it, modify it, sell it, give it away to your friends (or to anyone), you can do anything. There are several free licenses which handle these cases in a different way (e.g. GPL, LGPL, Apache License, MIT License, Boost License, Vim License and so on). They're sometimes called copyleft licenses (as opposite to copyright term). If you're interested, here's the wiki page comparing most of free licenses: http://en.wikipedia.org/wiki/Comparison_of_free_and_open-sou...

Please note that it doesn't mean that the software is being given away "for free (gratis)" (but usually it is) - it only means that once you obtain it, you can do anything you want with it.

Oh, and a mandatory link when we're talking about Free Software: https://www.youtube.com/watch?v=9sJUDx7iEJw