In theater, an understudy is a performer who learns the lines and blocking/choreography of a regular actor or actress in a play. Should the regular actor or actress be unable to appear on stage because of illness or emergencies, the understudy takes over the part. Usually, when the understudy takes over, the theater manager will make the announcement prior to the start of the performance.
In the opera world, the term cover or covering is used.
More recently, the term "understudy" has generally only been applied to performers who will cover a part, but still regularly perform in another role within the show; usually a minor, extra role.
Read more about Understudy: Similar Tasks, Multiple Understudies, Notable Examples