Belial's Wand is a magical weapon in the shape of a wooden stick covered with red runes. Its main function is to dispel the red and green lemniscatic wards on the doors of Charles Randall's Vicarage which are supposed to keep Adam from entering. They are, thus, of a specific nature, notably wards of passage.
The Wand lies hidden under the doormat and is required to be used in conjunction with the magical torch which is found in the small cabinet next to the vicarage entrance, the latter of which will render the wards visible in the first place. It's essential, thus, to have both of these items equipped at all times while exploring the edifice, as trying to open a warded door will inflict significant damage.
Adam: Magician's Wand maybe?
Adam: So this wand dispels Wards.