"The American and the girl with him" are introduced in this curiously off-hand phrase, as though it is merely an accident that they happen to be together. We are told almost nothing about them. The fact that they are continually described as "the man" and "the girl" suggests that he is the older of the two. We know that he is American, while her nationality is not mentioned. He remains nameless and, while she is called "Jig," this seems more like a nickname than a name.
We infer that the two are lovers. We do not know if they are married, though the way in which they discuss their life together and the possibility of an abortion suggests that they are not. They seem to be wealthy enough to travel around, as the girl says, looking at things and trying new drinks, without the need to work or worry about money.
Their relationship is clearly an unhappy one. The man is bored and irritated. He seems to want the girl to abort the child because a child would be an inconvenience and an incumbrance to a selfish, shallow lifestyle which he does not even enjoy. The girl is restless and ill at ease, vainly trying to return to an earlier stage of their relationship when the man was more demonstrative and seemed interested in her. She wants to know whether, if she does as he asks, "you'll be happy and things will be like they were and you'll love me?" He attempts to reassure her that he loves her anyway, but she does not believe him and neither does the reader. The bleakness of their conversation shows how entirely dead their relationship is. It is certainly not going to be revived by the death of her child.
It seems that the relationship isn't particularly fulfilling, especially for the girl, Jig. The man wants to "try and have a fine time," but Jig seems to find his lack of feeling to be somewhat upsetting. She says, "That's all we do, isn't it—look at things and try new drinks?" When the man first brings up the subject of abortion, which he does not explicitly name, Jig suddenly "looked at the ground the table legs rested on." She continues to remain silent while he goes on about how easy and simple it would be. The fact that the man is never named and that the girl is really only referred to by what seems like a nickname ("Jig") seems to indicate a certain amount of figurative, emotional distance between them. Further, the man does not really comment on Jig's association of the hills with white elephants (which is an idiom that refers to an unwanted and potentially expensive gift). He does not pick up on her mixed feelings about what he's suggesting, how she really just wants to be assured that he'll love her; it seems to me that she wouldn't even need such reassurances if she felt truly secure in his feelings.
In this story, Jig and her lover have a very strained relationship. Just as they are stuck in limbo at a train station, so they are also stuck in limbo in their relationship: it simply isn't going anywhere, which is represented by their conversation going in circles.
Jig is pregnant, and her lover, the father of her child, wants her to get an abortion. She doesn't want to do this. None of this is said directly; part of the problem this couple is having is that neither will speak openly. The man says over and over that the abortion will be easy, but he also says it's a matter of whatever Jig wants. He says:
I don’t want you to do it if you don’t really want to.
It is obviously, however, not whatever Jig wants, as the man wants the abortion; the more he repeats that it's whatever Jig wants, the more it is clear that he wants to impose his own will. Jig, in turn, keeps repeating what he says in a way that becomes belittling and mocking. She also says they could have "everything," while all he wants is to go back to the way everything was before the pregnancy.
Despite the flat dialogue and the lack of narrative markers to let us know how the two are speaking to each other—we don't hear words like "angrily" or "sarcastically" in this very spare story—it is obvious that the couple's relationship is corrosive and unhappy.
In the short story "Hills Like White Elephants" by Ernest Hemingway, the woman, Jig, and the American are lovers, engaged in a sexual relationship. We do not know if they are married, but the language and behavior of the couple suggest they are not. Jig is pregnant with the man's child and the man is urging her to get an abortion, while she is somewhat ambivalent about the process. The man is uncomfortable with the idea of fatherhood, because he has been traveling around Europe enjoying himself, and thinks that the responsibilities of fatherhood would get in the way of spending a life attending parties and trying out new drinks.
The story is set in a railway station where they are talking obliquely about this life decision. The main characteristic of the relationship is that the man and woman have very different goals in life, and much of the conversation reveals this conflict.