It is a collar which will, upon being worn outside the pre-programmed area, explode, consequently killing its wearer. It is placed on the Courier at the beginning of the quest Still in the Dark to make sure the Courier complies with the Brotherhoods orders. Note that this collar also records what you say, sending a live feed to the Brotherhood of Steel. The Courier also cannot fast travel while it is on. Once the first part of Still in the Dark is completed, it disappears from the game permanently.
The control collar appears in Fallout: New Vegas.