Backup roles are typically linked with a primary role, and don't get to use their action until an/the active role of the same name dies. Backup Cop and Backup Doctor (sometimes called Deputy and Nurse respectively) are common roles to utilise this modifier; but Trackers, Vigilantes, and Roleblockers (amongst others) are all roles that occasionally might have a Backup.
If a Backup role is linked to a modifier or passive ability, it instead prevents the modifier or ability from having any effect until a player with that modifier or ability dies. For example, a Backup Miller investigates as town at the start of the game, but will start investigating as though they were a Mafia member once a Miller has died. (This effect happens "upon the flip", i.e. at the end of the night or day phase in which the backed-up role dies; modifiers don't suddenly kick in in the middle of night action resolution.)
Most moderators design games with Backup roles to reduce swing. Having a Cop and a Backup Cop is a simple way to ensure a good chance of that investigation power to be successful, as opposed to a game with just a Cop, which is subject to a Day 1 lynch or Night 1 kill, completely eliminating that ability.
Some mods have also designed games with a Backup existing without the primary role present, which typically serves to sow seeds of misdirection about the setup for the individual player and sometimes the town if that player dies. A Backup in a game without a primary role present is essentially a Named Townie. However, some moderators find this practice in distaste - either because the backup role creates a violated expectation of a primary role existing in the game, or because the backup-with-no-primary trope has been overdone.
Backup is an acceptable modifier under Normal guidelines on mafiascum.net, both with and without its primary role present. Nurse and Deputy are acceptable names for Backup Doctor and Backup Cop, although they are not required.