To do something 'out of the norm' is simply to do something that might be perceived different or unusual; or 'outside normal' (which would sound awkward to say). Anything that is considered unusual, unorthodox, or unexpected can be considered 'out of the norm'.

1. Losing her temper in public like that was totally out of the norm for Jane. She is normally very reserved.
2. The doctor assured him that the rash on his arm was nothing out of the norm, and that it would go away on its own.
3. Having such warm weather in October is outside of the norm. It's usually freezing!
4. The police noted the man's abnormal behaviour on the day of the killing. It made him the chief suspect in the case.