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1.
Refers to a secret online relationship that someone has with a girl on a social networking site(like Facebook) Usually the guy has many girls that he converses with and likes to be "officially" single but enjoys the conversation with a 1 or a few special girls. The girlfriend in a box is kept entertained by long and frequent conversations in a chat box forum while the others are openly flirtting on the Home page and wall of the guy.

In real Life: it refers to a girlfriend that a guy keeps as a convienence. when he is too busy; he likes to think he can just put her away in the closet like a toy in a box and take her out when he is bored or has nothing better to do.
Him: "Baby Girl, U know I love you. No 1 owns me until I say so. U C my status right? single. It don't have to be complicated. we R good here in the chat."

Her: "I guess i'll be your girlfriend in a box until U say we are going public"
by Tonak's plaything June 13, 2012