Her blends together two of the top things on my cinematic favourites list: the soft sci-fi romance of Eternal Sunshine of the Spotless Mind and Scarlett Johansson at the top of her game (but she'll still never top Lost in Translation). Spike Jonze, through incredibly considered writing and directing, touches on all the things about those films that speak to me.
It deals with a couple of themes at once, and manages to juggle them pretty well even if it does come out at the end not really saying anything definitive at all. But I think that's kind of the point, there aren't any clear answers to the questions it asks. For instance, there's obviously a message about how invasive technology becomes in our social lives. Theodore is often surrounded by people but completely oblivious to all of them because his mind is buried in his phone. It's a common criticism of social networking, we're all so busy speaking but not actually talking to each other. Is it a real connection if it's just facebook comments? Is it a real connection if you'll never actually meet the "person" you're talking to? Does it even matter if it's "real", and who decides what's real?
Technology and its implications are only the sci-fi elements on stage though. The more personal things Her deals with are about relationships. Loneliness and overcoming and accepting our past mistakes are big issues for everyone involved in the cast. The only really clear message that Spike Jonze puts out with the film is that it's all about the journey: all the ups and downs matter and shouldn't be forgotten, it's not just about aiming for happiness and getting depressed when you miss.