In the full plot of Terminator 3, John Connor and Kate Brewster fail to stop Skynet, and the film closes as the nuclear attack of Judgment Day begins. Everything below gives away the film.
The chase starts at Kate's animal hospital, where the Terminator pulls John and Kate out of reach of the T-X. The trio then digs up a weapons cache that Sarah hid in a mausoleum. Somewhere along the road, the Terminator tells them they only delayed Judgment Day rather than preventing it. He also reveals that in the future it was Kate who reprogrammed him, a fact that binds her to John's fate.
Kate's father, General Robert Brewster, runs a military program at Cyber Research Systems. A fast spreading computer virus is tearing through networks, and under pressure to stop it he activates Skynet. The virus and Skynet are the same thing: the system becoming self aware. Brewster then points John and Kate toward Crystal Peak, which he believes is Skynet's core. Soon after, the T-X wounds him and seizes control of the company's machines.
The hunter then turns the protector into a weapon. The T-X takes over the Terminator and orders him to kill John. He resists by forcing his own shutdown, which buys time but not safety, because the T-X recovers and resumes the pursuit. Once the Terminator restarts, he crashes a helicopter into the T-X at Crystal Peak. With his last fuel cell he destroys both himself and the T-X, and the blast keeps the bunker door from closing, which lets John and Kate get inside.
The bunker is not what Brewster described. Crystal Peak is an old fallout shelter and command post, and Skynet is software spread across networked systems with no single core to destroy. It launches a worldwide nuclear attack. John accepts that Judgment Day cannot be stopped and begins answering the frightened radio calls from survivors.
