The fact that the woman in the story, Jig, has white elephants on her mind leads me to believe that she views her unborn child as something that other people would think of as a gift but that she thinks of as a burden. The phrase "white elephant" is an allusion to a story about the king of Siam. It is said that he would give a white elephant as a gift to courtiers he did not like; white elephants were rare and unusual, and, therefore, one would not put a white elephant to work—one must simply feed and care for it and keep it healthy. This required a great deal of money, so possession of a white elephant would drain a person's fortune dry. Thus, it is a gift that turns out to be a curse rather than a blessing. In the Hemingway story, Jig says that, in the sun, the hills in the distance "look like white elephants." It's rather an odd thing to say, and it seems to betray her thinking: an unplanned pregnancy could certainly feel like a burden rather than a blessing, especially to a woman who is unmarried in the early twentieth century.
Further, the man clearly wants her to abort the fetus, saying that "it's perfectly simple" and is "really an awfully simple operation." He says, strangely, that "It's just to let the air in." However, Jig seems more reticent. She says things like, "It's ours," and "Doesn't it mean anything to you? We could get along." Thus, it seems that part of her may want to keep the child; perhaps she is more serious about the relationship than the man is, or maybe she has personal reservations about abortion. We never know. His insistence that she get the abortion, however, makes her wish he would stop talking, and she even feels that she is going to "scream" if he doesn't. So, there is at least some part of her that wants to keep the baby too.