The main driving force behind it is that anyone can edit the lyrics, and even better, anyone can ANNOTATE the lyrics to explain what certain sections mean.
Let's take for example the lyrics for Mumford & Sons' "The Cave": http://rock.rapgenius.com/Mumford-and-sons-the-cave-lyrics
I looked up this song one day trying to understand more of the allusions made in the song; I know the title itself alludes to Plato's 'The Cave' and wanted to delve deeper. Because of this site, I can see that Verse 3:
> So come out of your cave walking on your hands
> And see the world hanging upside down
> You can understand dependence
> When you know the maker's hand
is an allusion to St. Francis.
Most of the time when Rap Genius ISN'T the top result for lyrics when I google, I facepalm and go directly to their site.
I should emphasize here that this overly positive post isn't intended to condone their shady, spammy blackhat SEO tactics, but damnit if they aren't the BEST lyrics site by a fair margin.