A spur-of-the-moment decision to do something that you should not be doing, which you then deny when someone finds out about it by saying it was completely on accident.
Girl 1: Did you steal my favorite shirt? I found it in your room
Girl 2: Oh! Uhh, I must have, um, packed it in my bag by mistake when I was leaving your house! It was on accident!
Girl 2: Yeah, right, accidentally on-purpose!