What exactly is a full parry and how does one go about doing it?
If you're familiar with fighting games, you usually block by holding the joystick/d-pad "back." To parry an attack in Street Fighter 3, you have to tap "towards" just as an attack is about to hit you. Since you're tapping towards, you're obviously not blocking. If you mess up the timing, you eat the attack. In that Daigo video, if Daigo just blocks, the super attack will still do enough block damage to kill him. So Daigo has to parry every single hit. It's hard.
This video shows what the super looks like before parrying every hit (30 seconds into the video, ending round 1):
http://www.youtube.com/watch?v=54l0jfGhRss&feature=related
Daigo may have done more impressive things, but nothing is as iconic as that. The moment is just perfect: the combination of the difficulty of doing it, the high stakes of the match, knowing that one miss and he'd die, going straight into his own super combo to come back and win the round, and the sheer wow factor.
Having perfect timing in a single player game against the patterns of a computer in the comfort of your own home is one thing. Being able to have perfect timing and execution on as big a video game stage as Evo in front of that crowd with the tournament on the line against arguably the best American fighting game player... that's a bit more.