Others may have additional virtues but from my perspective, the big one is that, when hiking in the rain, your behind doesn't get as sweaty.
Also, when I'm wavering between pants and shorts, I'll take shorts and my chaps. That way, if my legs feel chilled at any time, I just throw on the chaps. Additionally, I wear them with my poncho to keep my legs dry in the rain.
Oh, and if you're brave, hang free and wear the chaps by themselves!