The mask is worn by unnamed white glove society workers. It is stated in-game that the intention of wearing the masks is to create an atmosphere of mystery with regards to the patrons' impression of the hotel.
Equipping this item singularly does not create a pop-up notification that the character is dressed as a member of the White Glove Society. However, un-equipping it when worn without the other component notifies the player that they are no longer disguised as a White Glove member.
When given to Veronica, she will equip the mask and then offer to teach you a new unarmed attack move as if you gave her a dress.
Xbox 360 One of the most useful bugs in Fallout: New Vegas includes the simultaneous use of the White Glove Society attire and the White Glove Society mask. In fact you can get idolized with almost every faction. You must wear the attire first, then put on the mask. Now don't take off the attire, but equip a faction outfit over it. After this remove everything. If everything has been done correctly, check out your faction relationship and you should be idolized by almost everyone. [verified]
Xbox 360 There is a bug where the disguise is not removed with the mask, permanently setting your reputation with several, high-profile factions to neutral. Possible causes and solutions are available here. [verified]