Cat was built by the Seventh Doctor because he was tired of travelling alone and all his invitations had been declined. She thought she was from the 20th century because many companions did come from that time. At some point she faced the Cybermen and Gelsat creatures alongside the Doctor. Because of her true nature, she had gaps in her memory.
When caught short of mercury for the TARDIS's fluid links, the Doctor and Cat stole some from the Wierdarbi. Cat proved her resourcefulness by releasing a swarm of prototype robots from the Doctor's workshop as a distraction. She and the Doctor escaped, but the Doctor lost his precious Gladstone bag. Cat thus suggested a shopping expedition, so they went to a marketplace on the planet Haven.
While the Doctor entertained, Cat went on a shopping trip. They were then plunged into an adventure that caused Cat to think about her memory gaps. They eventually ended up on a dangerous spaceship that only an android could save, but it would be destroyed. It was then the Doctor told Cat the truth. Cat presumably died saving the ship. (PROSE: Companion Piece)