The T Party room was a room, setup in whatever city they are at tour with, where Taylor Swift, her band and friends hang out with fans. Taylor called it their home base.
The T stands for Taylor, her mother, Andrea Swift, coming up with the name.
Her mother would go into the crowds during Taylor's performances to find fans to invite backstage to meet Taylor, for free!
There is a rainbow ceiling, foose-ball table, ping pong table, two giant couches, and her favorite part was the picture column which has pictures on it from everyone from the tour.
The room was named Club Red during the Red Tour, Loft '89 during The 1989 World Tour, and the Rep Room during the Reputation Stadium Tour.