History
Kate Brewster had met John Connor when they were children. They were close to developing a relation but the events of T2 prevented that from happening. Years later, Kate becomes a veterinarian and meets up with John when a T-X Terminator targets since she will become of the resistance leaders in the future.
After meeting back up, John figures it is because they were fated to be together. They later become married and begin the resistance against Skynet.
Other Media
Films
Claire Danes played Kate Brewster in Terninator 3: Rise of the Machines.
Bryce Dallas Howard took over as Kate in Terminator Salvation.