"Psycho Jack" is the alternate form of Jack Bauer from 24. He comes out from time to time when Jack is in great mental distress. Typically, when regular men are faced with a situation that they cannot mentally handle, they fall apart. Jack Bauer is no regular man, and when he is faced with such a situation, he struggles for a short time with the burden; slowly you can see a change in his eyes. Then Jack is then overtaken with an intense, psychotic, murderous rage.
While in this rage, Jack has no concern for his own life, can't really feel pain, shooting him just pisses him off even more and he will not stop until every single person he is currently facing is dead. His fits of rage typically only last a few minutes, but while fully raged he is without fear, hesitation, and all of his senses are heightened to near superhuman levels.
In Season 1 we saw his transformation to Psycho Jack for the first time. Nina tricked Jack into thinking his daughter had been murdered by Victor Drazen and his men.
You see the event nearly broke Jack, he even shed a few tears for the loss of his beloved daughter.
Then you saw a change in his eyes, and he drove a van into the warehouse were Drazen's men were waiting for him. He proceeded to kill every single person in the warehouse and confronted Drazen. He then proceeded to shoot Drazen 12 times until his gun ran out of bullets. With Drazen dead, Jack returns to his normal state.