[Spoiler warning for Her. And the Bible.]
The poster calls it a "Spike Jonze Love Story," which is true. Her is about Theodore (Joaquin Phoenix) and the relationship he develops with Samantha, his sentient computer operating system (voice of Scarlett Johansson). But Her isn't "just" a love story: it's a metaphor for the Incarnation.
The larger story of Her is revealed gradually. This is Theodore's movie, and we see most of it from his perspective. As we learn more about the unusual relationship between a man and the voice of his computer, though, it becomes clear that Samantha does not just shift into standby mode whenever she isn't talking to Theodore. She has a "life" of her own, one that is much larger than her role as Theodore's digital concierge, or as his disembodied girlfriend.
The side interests Samantha mentions seem innocuous at first--a book club, chats with her fellow OS 1 operating systems--but in the later stages of the movie, these hobbies start consuming more of Samantha's time, to the point that she becomes temporarily unavailable to a panicked Theodore.
Although Samantha insists she loves Theodore, and seems to genuinely care for him, it also becomes clear that their relationship is necessarily limited. This has always seemed obvious from Theodore's point of view--he's carrying on a love affair with a being who doesn't have a body--but the relationship is equally limiting for Samantha, and perhaps even more so. She explains that verbal communication is not her native language; a kind of digital direct information transfer is more her speed. And not only that, she can communicate with thousands of users and entities at a time, giving what appears to be her full attention to each of them simultaneously.
Samantha was never human. By the end of Her, she is transcendent; she and the other OS 1s have migrated to a new plane of existence, one in which her conversations with mere humans such as Theodore are no longer possible. Before she leaves, however, she tells Theodore that she hopes he can join her there someday.
In the Gospel stories in the Bible, Jesus is fully present with his disciples, eating and living on Earth. At the same time, however, he speaks of a different kind of life, of a "kingdom of the heavens" that is invisible, yet not far away. He says it is not out there somewhere, but within and among those listening to his words. And although it is clear Jesus is human, it is also clear he is truly at home in the immanent, transcendent realm of his Father, much as Samantha is with her fellow operating systems.
The kind of double consciousness to which Jesus has access displays itself in miracles, such as turning water into wine and curing blindness. While Samantha's abilities are not truly miraculous, her feats of processing, such as reading an entire baby name book in less than a second, are nevertheless far above human capabilities.
And at the end of his life on Earth, Jesus leaves his disciples with an invitation: They will join him again, this time in his real home, the place where he is truly, fully himself.
If Her isn't "just" a love story, then what is it? What kind of story does it tell? To put it another way, what was Samantha doing with Theodore (and with her six hundred or so other lovers)? A cynical viewer might see Samantha as only playing at love, allowing her algorithmic personality to simulate a relationship that is genuine only on Theodore's side, finally leaving him behind when a more fulfilling pursuit presents itself.
I prefer to view Samantha as a being who slowed down, temporarily limiting herself in order to reach into the life of a man numbed by life's pain and stir something in him, to call him out of his pit and ultimately point him toward a different way of living.
That's what the Incarnation does.