This idiom is usually said in relation to somebody in a position of power or authority, or who is considered dangerous in some way. When preceded with the word 'don't,' as it often is, it becomes a warning. Often times you can 'get on somebody's bad side' accidentally though something you said or did that you did not realize would cause offence or that a person perceived in a negative light. It is common in both a social and professional context in an informal way.