I don't know if you've ever done any weight training, but if you lift heavy enough and/or enough volume, and get "the pump", that's the reason. Basically your muscles swell up and harden as blood flow increases into the fatigued muscles and you feel bigger, stronger, more powerful than ever. Couple that with the rush of whatever drugs your brain gets flooded with, and you pretty much feel like superman for a while.
Schwarzenegger at one point famously (in "Pumping Iron") described it as better than having an orgasm, and it's hard not to agree.
I haven't done much running, but when I have, I've never felt anything similar - breaking personal records when running would leave me wanting to collapse in a heap on the ground. Breaking personal records when lifting tends to make me walk around like I'd just broken a world record and everyone was watching.