Thinking about the question while doing P90X's plyometrics routine today, the psychological benefits alone make it, for me, an answer that is capable of being comprehended. Everything else becomes a cinch by comparison. There is nothing in my entire week, no matter how full my work plate is, how unfamiliar I am with a girl I'm seeing, or how daunting quantification of some blogging idea might be, that is nearly as formidable. So after an excruciating hour, I know there are easy buttons all over the place for the next 167. It scales daily as well, as it is the rare day indeed in which I don't get something of extreme intensity in.
The Derb pithily accesses the essence of it:
Life’s great law is that poverty and hardship build character; prosperity and security destroy it.Pushing yourself to your physical limits creates hardship, albeit of an artificial nature. But it beats comfortable flabbiness.
Of course there are other obvious physical benefits, like "performing everywhere better" in Tony Horton's words, and in that respect, I find distance runners to be tragically misguided--distance running keeps you thin and makes you better at... distance running, and little else. P90X, faddish as it may appear at first blush, builds muscle mass everywhere while simultaneously increasing both dexterity (I'm now able to keep up with Dominque, the guy in the back, throughout plyo, and I'm a bigger guy than he is) and flexibility, at least for those of us fortunate enough to reap the physical rewards of exercise.
Anyhow, I am able to relate exclusively to the psychological comforts an intensive workout (which, by definition, almost requires multiple fails) brings and suspect it is one of those things that is hard to understand until you've been there: