"She" is a subject pronoun (like "lei" in Italian) and "her" is an object pronoun (like "la" in Italian). So "SHE reads the textbook at school," but "The teacher gave the textbook to HER." Therefore, it is very appropriate that the movie is titled "Her" because the female "star" of the film is an object, not a subject! :-) So this was a deliberate word choice by the director of the film.

For me, when I see "she" I think of any woman or girl, perhaps someone random. However when I see "her" I think of someone more specific - not just any woman or girl but someone specific, someone important maybe.