Other contributors have said "What did people watch at rome circuses?" is the same question as "What is a circus in ancient rome?" If you believe that these are not asking the same thing and should be answered differently, click here
In ancient Rome a circus was a race track. Chariot races were held in them. They were uniquely built for the races with a "spina" or middle barrier dividing the track, around which the chariots raced.
If you mean the Circus Maximus, it held 150,000 people after the remodeling by Julius Caesar. The other circuses, of course, held less people because of their smaller size.