1. The way into the cavea of a Roman theater or amphitheater.

A cavea was the concave-shaped auditorium of an ancient open-air theater, which was often a semicircle of stone benches rising in tiers.

A cavea might be divided, depending on the size of the building, into one to three distinct tiers, called upper, lower, middle (summa, ima, media cavea).

2. A passage or opening in an ancient amphitheater or theater, leading to or from the seats; permitting large numbers of people to enter or leave.

A place for vomiting?

Vomitoria in ancient amphitheaters helped the audience to reach their seats quickly and then, at the end of the performance, leave at an equal speed (hence the name). Thousands of seats could be filled in minutes.

The suggestion that a vomitorium was the place for the ancient Romans to vomit during a feast has no basis.