"Hills Like White Elephants" is a story about the end of a relationship. The themes mainly grow out of this scenario.
One theme of the story is dealing with difficulty, or dealing with unplanned pregnancy. We see the couple in "Hills Like White Elephants" debating the proper course of action in dealing with an unplanned and unwanted pregnancy. This debate poses the man against the women. So we have a conflict of the sexes.
The nature of the couple's argument broaches thematic ideas related to the intractability of time (you can't turn back the clock), and the persistence of memory (you can't forget things on purpose) as the man tries to convince the woman that if she gets an abortion, the two of them can regain the easy and loving relationship they once had.
We also have an issue of a lack of communication or a lack of understanding, which can be seen in two places. First, the female character does not understand Spanish and so does not understand what the waitress is saying throughout the story. Also the couple exhibit this same lack. The woman does not agree and does not want to understand what the man is saying. And the man does not understand why the woman won't agree with him and why she bristles and acts with fickle impatience.
This is all open to interpretation, of course, as the story is quite understated.
One of the main themes in "Hills Like White Elephants" is talking vs. communicating. Although "Hills Like White Elephants" is primarily a conversation between the American man and his girlfriend, neither of the speakers truly communicates with the other, highlighting the rift between the two. Both talk, but neither listens or understands the other’s point of view. Frustrated and placating, the American man will say almost anything to convince his girlfriend to have the operation, which, although never mentioned by name, is understood to be an abortion. He tells her he loves her, for example, and that everything between them will go back to the way it used to be. The girl, meanwhile, waffles indecisively, at one point conceding that she’ll have the abortion just to shut him up. When the man still persists, she finally begs him to “please, please, please, please, please, please” stop talking, realizing the futility of their conversation. In fact, the girl’s nickname, “Jig,” subtly indicates that the two characters merely dance around each other and the issue at hand without ever saying anything meaningful. The girl’s inability to speak Spanish with the bartender, moreover, not only illustrates her dependence on the American but also the difficulty she has expressing herself to others.