They are a dark foil to the main character as they embody the movie's opposite theme or ideology.

A presence in the story, a personality and making them the antithesis of the main protagonist.

Being a good foil to a hero/being in tight with story main theme, but i would say that main thing is his charisma/atmosphere/presence. Your villain can be complex as hell but if they're not interesting to watch them in process - everything else becomes shallow.

It depends on the story, but generally these are the traits that make the best villains in my eyes: Understandable motivations, competence, relentlessness, charisma, evil actions

I also think that a good villain should have a clear rise to power arc and have some small defeats against the heroes. Nowadays, I find it boring how villains are just powerful and unbeatable throughout the movie and only get defeated in the climax. The heroes should claim certain victories against the villain at like the mid-point or something of the movie. This makes their conflict more engaging to watch and avoids making it feel one-sided or predictable.

Giving a hero fun and interesting fight, having great lines, voice and design, maybe some backstory here and there.