Um.... maybe its just the affects of alot of oxygen getting into our body real quick. The body is also pushing out alot of opiates to deal with the stress of your feet pounding on the ground.
Walking fast can get you there too.

In high school I normally ran 18 miles per day. The first 10-12 miles were a little strenuous, but after that it felt like flying.

I can relate. I do 45 minutes of high impact cardio every morning. Sometimes the euphoria kicks in within 10 minutes. I know that my mood lifts as soon as I start exercising, though sometimes it takes me half an hour of piddling around just to start. But by the end I'm always happy.

That's just me. When I was a kid I practiced holding my breath as long as I could. On the rare occasion instead of wanting to gasp for air, a feeling of ecstacy would kick in, and it seemed like I could hold my breath as long as I wanted and feel no pain. But I was a smart enough kid to tell myself that I'd better take a breath if I um...wanted to live a little longer.

I often run high so I'd have trouble differentiating.

So that's why these presidents that jog never get anything done...they're stoned all the time.

I've experienced this myself, although for me it's rare. One time, it happened to me when I was running on the beach after about three miles...it felt as though my movements were effortless and my physical being was an afterthought. ...sigh... It keeps me plugging away at running, which I'm not particularly "good" at. My family could tell you that they can notice my mood is significantly better when I get out there.

it's real. the endorphines released by the brain create the so called high. also, it may be the paying of attention to breathing while exercising which is meditation technique. it's likely a combination of these factors. it may be attributed to the meta-[beyond physical]physical thereby not quantifiable with the tools being used or which are available.