Like Facebook Girlfriend, a facebook wife is a false wife on facebook that you'd like to go out with, but you don't have a chance.
Sometime used to draw attention to 2 people, not as a couple, but as someone who has someone else.
Person1: dude, will you facebook marry me?
Person2: ohyeah, sure! i'd love to have a facebook wife <3
Person1: wanna facebook marry me so we get more attention?
Person2: yeah.. i've been single too long.. i need a facebook wife>_>
person1: your married now?
Person2: yeah, shes smokin, we do everything together. ;)
person1: ohmygodimsojealous... wanna go out sometime?