If you've ever ran over 10 miles at a time, you'll understand the need for compression clothing. It really helps alleviate chaffing and any discomfort caused by loose clothing.
I always feel like a Superhero when I'm putting on my Under Armour. Something about the stretchy spandex-iness of it just makes me feel like I'm gearing up to fight crime. That, combined with the fact that I wear my running shirts and shorts over the spandex, gives me the feeling of being Peter Parker, with his Spiderman costume hidden under his everyday clothes.
(Trust me, you don't want to see me in this stuff with nothing on over top - it shows every flaw you may or may not be aware of. I may be proud of my shoulders and chest, but I still have that pudge around the waist that looks HUGE when wrapped up like a sausage.)
The only downside to it is taking it off after a run - it tends to want to stay put, and wrestling with a sweaty, clingy thing is only enjoyable during sex. (And since I'm taking it off by myself, that only goes into awkward masturbation territory.) Still, it's better than chaffing.
On the bright side, if I happen to come across a crime in progress while out for a run, I'm suitably dressed for the occasion.