Archiving takes an act off your roster. They get no new offers and no broadcasts from you, and they drop out of your pickers and searches.
Bookings they've already accepted still stand and still need to be played. Archiving isn't a way to cancel work; cancel those separately if that's what you mean.
You can restore an archived act at any time, and their history with you is untouched.
You're archiving your own relationship with the act, not deleting them. The act profile belongs to the performer, and they may work with other agencies.