Away From Keyboard. Viewpoint that online life is the same to "in real" life. So instead of saying "irl" when referring to In Real Life, they say "when AFK". Or, instead of saying "oh I was not online" one would say "I was AFK".
Two rough examples
hello and good morning
Oooh, love that. Perhaps there's an even more general case that's more slick than AFKAORTPS, i.e. "away from keyboard and/or touch pad/screen" so tablets and "smart"phones are included?