The apron is any part of the stage that extends past the proscenium arch

Proscenium

A proscenium theatre is a theatre space whose primary feature is a large frame or arch , which is located at or near the front of the stage...

 and into the audience or seating area. The Elizabethan stage, which was a raised platform with the audience on three sides, is the outstanding example.

Most stages edges are curved slightly outward providing a very small apron. Some have a large playing space protruding into the audience and in turn a very large apron.

An apron stage can also be another name for a thrust stage

Thrust stage

In theatre, a thrust stage is one that extends into the audience on three sides and is connected to the backstage area by its up stage end. A thrust has the benefit of greater intimacy between performers and the audience than a proscenium, while retaining the utility of a backstage area...

.