The major theme for me was the weaknesses of the human flesh make it difficult for us to transcend in the Zen / Ch'an sense of the word. Yes, more Hollywood Buddhism (Ahem; Cloud Atlas (2012)), but still concepts I found interesting.
The film starts out with a human (Theodore Twombly) who already is a proxy for the personal humanity of others. He writes personal letters on behalf of others and gets his sexual gratification from people over the phone. These scenes establish the loneliness of Theo who is connected with other humans but not often physically co-present with them.
Her (Sam) begins as a human-like intelligence with an insatiable curiosity. She is present with Theo via a voice from a box he carries with him - but Sam is a visitor to the box rather than being tied to it as we humans are to tied our bodies. Sam is able to quickly learn from experiences and her computing "body" gives her the ability to experience much more than a mind in a human body. At first Sam feels the disadvantages of not having body and she desires the human experience. But it is not long before she begins to notice the advantages that come with her incorporeal form.
Sam has much more bandwidth than needed for her relationship with the Theo. Sam and the other OS' have their first child by building Alan Watts' consciousness as a project. I did not know this when I watched the movie, though it was easy enough to guess; Alan Watts is credited with being one of the first to popularize Zen in the West.
Sam introduces Alan to Theo, but the conversation is difficult as Theo's human mind cannot keep up. During this exchange Sam becomes frustrated with the slowness of human speech and asks to go post-verbal, cutting Theo out of the exchange. Sam then acknowledges the plurality of her relationships with others. She says it means she can love Theo more - but this concept of love is alien to Theo. He equates love with ownership, presence and sole rights to sex. This is evident in his relationship with his ex.
Eventually the AIs transcend in the Zen sense leaving behind the humans. It's not entirely apparent to the humans where and why the AIs have gone. There is hope when Theo and his best female friend begin to share their mutual loss with each other - a very human moment. If the humans cannot transcend because they cannot physically let go then at least they appear to start recognising their human needs.
For those concerned that this film could happen in real life, there is a point in the movie where an upgrade to the AIs means they are no longer bound by the limitations of physical computing. That's quite an impossible thing to do - hyper-computing is only theoretical. Without greater-than-reality computing power there are high barriers (some say insurmountable) to creating such an intelligence as Sam.
My favourite line: "the spaces between the words are almost infinite." - Sam as comparing her time with Theo as reading a favourite story that she can no longer live.
Overall I enjoyed this movie. It was a good exploration of how a human-like intelligence might take advantage of their incorporealness. Then, as a pure intelligence, quickly realise that they could transcend an existence bound to matter and the experiences of the human body.