The hills in "Hills Like White Elephants" are an area of raised ground which is symbolic of the raised stomach of the pregnant woman. They are also described with more vitality than the surrounding landscape.
They were white in the sun and the country was brown and dry.
The simile of "white elephants" being like the hills is an odd one. An elephant is large and being white rather than the typical gray makes the image more striking. This could be interpreted as the colloquial "elephant in the room," a phrase which refers to something everyone is aware of but everyone is reluctant to talk about it. This fits with the story because although the American and Jig are talking about a possible abortion, they are doing so in veiled speech.
"Well," the man said, "if you don't want to you don't have to. I wouldn't have you do it if you didn't want to. But I know it's perfectly simple."
In addition, the phrase "white elephant" means a valuable possession that is also a burden. And this burden is one that you cannot get rid of. This is an obvious reference to the unwanted pregnancy and the couple's discussion about possibly "getting rid of" the baby. The American dwells on the burden more than the value of the baby. The girl, Jig, is concerned about what having an abortion will do to her outlook on life. Still speaking in veiled terms, she suggests no matter what her decision is, something will be lost.
"No, it isn't. And once they take it away, you never get it back."