A Visitor is a type of character in the game. They visit the prison when the player is seated in the Visitation department - a room that allows you to talk to outsiders. This room can be used at anytime during the day, however, your heat can rise so it's best to do it during Free periods. In The Escapists 2, you can only be visited during Free Time; sitting in the visitor-department chairs during other routines will not cause a visitor to arrive.
Once they are both seated, they will engage in conversation, talking to the player like how a normal guard or inmate would. However, there's less interaction that can be done between the player and visitor, and the visitor does not help the player in any way towards their escape. In The Escapists 2, they will sometimes give you presents, which are simply random items placed into your inventory.