I do it to impress girls
actually, in somewhat seriousness, I rode my first century partially because I was recruited to do a charity century ride by a girl that I was flirting with at the time; and I first started to seriously contemplate brevet riding after another female friend was considering randonneuring and looking for a training partner. That person was too swamped with schoolwork to do any distance riding, but I've had fun with it ever since.
And, in complete seriousness, the things that I get out of distance riding is, as others have mentioned, the sense of adventure and challenge; a desire to explore and also gaining a deeper understanding of what my body's capable of when it's subject to extreme stress. The process that I first went through of plunging into a brevet series and going from a 200k to a 300k to a 400k and a 600k, and seeing how my body adapted to handling distances that I once thought of as impossible was tremendously addictive.
Even now, after doing such long distances, I still welcome doing centuries and 200k's because it still feels like there's some new discovery awaiting me somwhere along the ride. I want to find out what that is.