The birth skirt is an item used solely in the beginning sequence to represent the supposed point-of-view of a newborn baby. On a male character (i.e. James) the birth skirt takes the shape of a doctor's face mask.
The birth skirt is not obtainable through normal gameplay and can only be obtained with the use of console commands. It is only worn by the Lone Wanderer's mom during the birth sequence at the start of the game.