@Ryan T, I prefer to think of it in even simpler terms:
1. Your body won't let you get into positions it thinks you can't get out of.
2. You move yourself into near-end-of-range-of-motion positions and tense your muscles to demonstrate to your body that you _can_ be strong there.
3 Your body says, "OK, now that I've seen we can be strong there, I'm willing to go there, stay there, and relax there."
The beautiful thing is that you can't tense in truly the extreme end of your ROM, so you get close by going nearly as far as you can, you tense, you relax, and then you move a little further into that same direction and tense again - a few cycles of this and, voila, you've improved both your strength and your flexibility.
The even shorter version: get strong where you want to be flexible.