This normally refers to live performances on the stage or in the circus of the kinds found in the early 1900's. It might include trained animals, comedians, magicians, dancers, acrobats, and plays. Normally these are funny performances, not serious ones. "Circuit" implies that the people are moving from one place to another. They might spend a week performing in New York, then move on to Boston.

It may mean that more people saw them the more they travelled around.