An opinion is a belief or attitude about something that isn't necessarily based on facts. It's your opinion that dogs make better pets than cats, but your sister thinks that cats are superior. Too bad your parents' opinion is that pets are too expensive.
You may have an opinion about a celebrity that I don't share. There's no way to prove who's right and who's wrong. Those are our thoughts about her, and that's the way it is. Ironically, when a judge decides a case, his or her ruling is referred to as an opinion. Even though what the judge says will become a matter of law, it's still just their opinion, based on what was presented by the two sides in a trial.