Very basic plot outline:
The guy (I forget his name) who is running in the race has an exceptional ability and awareness. Because of this, he is becoming aware of the Matrix on his own. He gets to the point during the race where he knows it is not real and thus begins to escape. But because he hasn't taken the Red Pill, his output carrier waves aren't screwed and therefore the Agents can keep him pinned down.
It is left open to debate whether he actually freed himself at the VERY end or whether he just collapsed 馃檪