This association formed the circuit on which black performers were able to travel and perform in the 1920 United States.
There is a T.O.B.A. break step which is very commonly danced.
And many of the most visible swing band leaders and musicians worked on this tour, including: Fats Waller, Louis Armstrong, Duke Ellington, Chick Webb, Cab Calloway, and Count Basie.
More information can be found on Wikipedia at Theatre Owners Booking Association.
There’s also a history of T.O.B.A from Musical Geography as well as an overview of some of the black women who were on the circuit.