A nickname for the girlfriend of a friend who has him seriously pussy-whipped
Neil: "Yo Bob let's hit up the strip club tonight, I hear they have 2-for-1 lapdances."
Bob: "No...uh...I can't. My...uh...girlfriend and me are gonna have a threesome with this hot-ass chick, dude, it's gonna be awesome."
Neil: "Shut up. Everyone knows the wife wouldn't let you do that." (whip cracks)
Bob: "Yeah...we're actually...uh...knitting."
When you have a partnership as in a business and all partners are equal but there is always someone who has a little more control than the others and that is the wife of the partnership. Term also works in other groups such as friendships, etc.
All 13 partners have an equal share in the company, but everyone knows Mr. Smith is the wife.