I recently wrote about the FreeType license and its double license and why it was necessary. It's an interesting situation (for FreeType itself) because there's the GPLv2 and a second Free Software license involved -- the FTL, which is basically a 3-clause BSD license with attribution required.
Often, though, when we talk about dual licensed we mean a situation where one license is a Free Software license and the other is a fully proprietary one. Bear in mind that the 3-clause BSD license allows proprietization as long as you satisfy the attribution clause and the license distribution clause, so it's not a world of practical difference, but one of intent. The suit filed around Palm's PDF viewer on the Pre illustrates the effect differences of intent can have.
One way you can look at dual-licensed software is that you have "the usual license" (which in our context is a Free Software license, probably some version of the GPL) and that for some users who cannot abide by the terms of that Free Software license, you sell exceptions. Richard Stallman writes on the subject -- I found it via groklaw, where also one of the first comments uses the phrase "selling indulgences," which I think is much more evocative.
So the point is that if you are the copyright holder -- the sole copyright holder, because you need to have the right to re-license the code -- then you can sell an indulgence to someone who cannot abide by the Free Software terms, but whom you consider worthy to use the software nonetheless. Yes, that's plenty subjective. My phrasing is also slightly wrong, because you don't have to be the sole holder: there are other ways of ensuring that you can grant the indulgence even with multiple rightsholders (a contract or license grant would do). In any case: you can do this for specific reasons while still supporting and producing Free Software.
This is also RMS's pragmatic point: while the FSF does not follow this practice, that doesn't mean others cannot while still being "ok". And I think that's good news for GPL'ed libraries out there. For users of GPL libraries, bear in mind that intent matters, and that the GPLv3 offers a grace period that the GPLv2 does not -- and that might be important when dealing with entities whose intents are not entirely clear.