A fly (short for fly-front) is an opening on the crotch area of trousers, closed by a zipper (often), or buttons. On men's garments the fly always opens to the right. On women's garments it may open either to the left or to the right.
A fly can also be on other garments, like the paletot coat of the 20th century, where it is the front opening that can be secured close and is covered hidden by fabric.
Trousers have varied historically in whether or not they have flies. Originally, trousers did not have flies or other openings, being pulled down for sanitary functions. The use of a codpiece, a separate covering attached to the trousers, became popular in 16th-century Europe, eventually evolving into an attached fall-front (or broad fall). The fly-front (split fall) emerged later.