Any situation where you have video which you just want on the big screen with zero hassle. Easier to just "flick" the video onto the screen rather than "ok, I've got it on my iP*, now either everyone huddle around the little screen or give me a few minutes while I try getting it on my ATV..."
Likewise for taking stuff to someone else's TV (their home, conference room, etc.): just take the ATV, plug it in, play from iP*. Maybe not that much different, but easier to take a phone & "puck" & 2 cables instead of bigger adapters/power-supplies/laptop/etc. (Still waiting for direct iPad-to-HDMI cable though, along with iPad-to-VGA/composite/component which works regardless of app.)