If I open the friends list interface, I can click the little gem at the top to set my current status:
I had assumed that these were merely cosmetic, but last night a friend was unable to join my game because I was set as "busy." I don't know if there's anything else that happens as a result of this, though.
What's the difference between Available, Away, and Busy? Do any of these options allow me to "hide" my online status, say if I wanted to play solo and not show up online?