So, don't mean to quibble, but if the movie is called Her, why does the DVD box have a picture of Him? Just wondering.
Also, just kidding. The titular character is an "OS" (Operating System) installed on the computer of the pictured Theodore Twombly (Joaquin Phoenix). He's on the bitter end of a recent divorce. He's good at his job (which seems to be ghost-writing sentimental letters for people too busy or too inarticulate to do so themselves), a gig which is lucrative enough to move him on up into a deluxe apartment in the (Los Angeles) sky. But he's desperately lonely and emotionally shut down.
But the Her OS, aka Samantha (voiced by Scarlett Johansson), changes all that. After a few seemingly perfunctory questions, Samantha springs to artificially-intelligent life. She would pass the Turing Test without breaking a CPU sweat, and she quickly goes from her initial role as Theodore's assistant, to confidante, then friend, then (yes) lover.
I kind of knew most of this going in, due to trailers and things heard on the street. I was skeptical: you can make a whole movie out of this idea? Yes, it turns out you can, if you're a filmmaking genius like writer/director Spike Jonze.
Aside: I think the movie assumes near the end that the viewer would recognize the significance of the name "Alan Watts". Really? I did, but I'm a geezer who read a lot of goofy stuff when I was young. I can't imagine a lot of other potential viewers being in a similar position.