Girlfriend mode is an unofficial term for a mode of playing the game Borderlands 2.
The skill tree is called Best Friends Forever, what lead designer John Hemingway dubbed the "girlfriend mode".
"The design team was looking at the concept art and thought, you know what, this is actually the cutest character we've ever had. I want to make, for the lack of a better term, the girlfriend skill tree. This is, I love Borderlands and I want to share it with someone, but they suck at first-person shooters. Can we make a skill tree that actually allows them to understand the game and to play the game? That's what our attempt with the Best Friends Forever skill tree is."
Randy Pitchford, the studio president, defended the company against sexism charges, saying it was not an official name.
Stephen Totilo at Kotaku suggested that it should be called "co-star mode", from Nintendo's Super Mario Galaxy:
The word 'co-star' elevates the status of the second, presumably less-skilled player. It clearly labels them as something other than the best player. They are not the 'star', but they are the guest, the visiting celebrity, the fellow great. They’re the celebrity walk-on in a sitcom or the other actor who isn’t being interviewed at the moment. They may be a mere supporting actor, but 'co-star' makes them sound so much important. It’s better than 'girlfriend mode' or any other construction that would label the second player as inferior to the first (see: 'casual mode,' 'person-who-sucks-at-games mode').
Daniel Nye Griffiths at Forbes explored the connotations of the term and how it relates to the so-called fake geek girls issue, and also relates it to the So simple, your mother could do it phenomenon.