The title of this story is a simile. The girl introduces this simile near the beginning of the story, as seen in the following passage:
[The Waitress] put the felt pads and the beer glasses on the table and looked at the man and the girl. The girl was looking off at the line of hills. They were white in the sun and the country was brown and dry.
“They look like white elephants,” she said.
“I’ve never seen one,” the man drank his beer.
Why the girl says that the hills look like white elephants is not entirely clear. It’s possible that, in “looking off at the line of hills” that were “white in the sun,” she sees that the white hills vaguely resemble the shape of an elephant’s head or body.
Some scholars believe that she compares them to elephants as a nod to the phrase “the elephant in the room,” and that this is her way of indirectly bringing up the fact that she is pregnant and needs to decide whether to have an abortion or not. That the man responds “I’ve never seen one” may, in turn, be his way of communicating that he wants the woman to have an abortion (by resisting her youthful imaginations and shutting down the conversation).
It's also possible that the simile is playing on the term "white elephant" as a way of referring to something unwanted and burdensome. Although this usage of the term isn't widespread, it can be used to talk about a piece of property that isn't valuable because it requires too much upkeep—it can also refer to an object that is of no value to its owner but would be valuable to other people. Both of these interpretations resonate thematically with the fact that the man doesn't want a child (and with the fact that the girl herself is unsure whether or not she wants a child). Still, though, Hemingway’s language is so sparse that it is impossible to know what, exactly, the girl means when she compares the hills to "white elephants."
