The tight, stretchy, one-piece garment that gymnasts and dancers wear is called a leotard. If you take a ballet class, you may wear a leotard and tights.
Leotards are worn by performers and athletes of many types, including figure skaters, ballerinas, acrobats, superheroes, aerobics instructors, and more. While a leotard leaves the legs bare, a unitard covers the legs as well. The French acrobat Jules Léotard is credited with inventing the leotard, although he called it a maillot. The leotard came to be named for Léotard in 1886, long after his death.