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"It is likely that in his long freefall of more than five minutes, he will exceed the speed of sound - the first person to do so without the aid of a machine."

If he can reach 120k feet, I bet there is a machine involved in the process. Why not just say he's the first person to do it through freefall?

They mean his acceleration will be without the aid of a machine.
Again, it's not true. He's just converting the potential energy stored with the aid of a machine into kinetic energy.
If you are going to be this pedantic, then even if he plans on growing wings and flying up there, you will still bitch because the meal he plans to eat the night before will be harvested by combine.
From a quick Google search, the terminal velocity of a human being is roughly 120 mph. The speed of sound (at sea level) is 761 mph.

How is this feat possible?

My thoughts exactly...I'm sure he'll be carrying extra weight but I still don't see how this is possible given a certain terminal velocity, like you said.

*Edit...wikipedia says current world record is 614 mph set by Joseph Kittinger. He used the head down method in high altitude, less dense air. That's still not supersonic though.

Kittinger wasn't as high up, the extra height should give Baumgartner more time to build speed.
The terminal velocity is much higher in this case because the skydiver is assuming a position that minimizes drag and the air is much less dense at the altitudes in question. Additionally, the lower temperature reduces the speed of sound in a smaller but still significant degree.
The terminal velocity in the stratosphere is significantly higher than at sea level, and the speed of sound is lower, at around 670 mph. Joeseph Kittingers' record was 614 mph, which is not that far off the sound barrier.

Pilots have ejected out at Mach 3 from a SR-71 http://www.alexisparkinn.com/sr-71_break-up.htm

In that accident, the pilot ejected without major injury, but the co-pilot was killed.

Excellent article. Note though that the pilot did not technically eject, his ejection seat was ripped out of the disintegrating plane intact by aerodynamic forces. Though the experience is probably applicable to the case where a pilot were to intentionally eject at Mach 3.
In addition to the reduced air density at altitude (as others have mentioned), body position, weight, and clothing also have a lot to do with terminal velocity. A light person wearing baggy clothes in a belly-down position might fall at only 90 mph, whereas a heavy person wearing skin-tight clothes in a head-down position could fall at 170 mph. (speeds given at lower altitudes, close to the ground)
He's being sponsored by Red Bull (http://www.redbullstratos.com/). Their marketing video is actually really cool, it includes plenty of footage of Kittinger.

http://www.youtube.com/watch?v=PyGmTV0q2kY (make sure you switch to HD)

I used to think that Red Bull just put their logo on cool stunts, but it turns out that they have a really competent team of engineers and fabricators to pull this off. In fact, Joeseph Kittinger, who holds the record currently, said they were the first crew to approach him that sounded like they could do this without killing someone (since 1960!), so he's actually working with them on this.