 It acts as an antechamber between the exterior and the interior structure.Often it connects the doorway to a lobby or hallway.It is the space one occupies once passing the door, but not yet in the main interior of the building 

Although vestibules are common in private residences, as a modified mud room, they are especially prevalent in more opulent buildings, such as government ones, designed to elicit a sense of grandeur by contrasting the vestibule's small space with the following greater one, and by adding the aspect of anticipation.