The hills operate in a number of ways. Let me add one more.
Before the woman became pregnant, the relationship was, most likely, far more easy, fun, relaxed, and loose. Before the pregnancy, when the woman said something as simple as 'those hills look like white elephants' it was enough to be amusing and diverting for the carefree couple. Now that the woman is pregnant, she is no longer carefree and she misses the times when the 'hills comment' might have been enough to distract and entertain the man. So, the white hills are a reminder of the way things were in better, easier, lighter, and more imaginative days before she became pregnant.
The hills can also symbolize the ups and downs that relationships inevitably face. These trials and tribulations are a part of any relationship.
The hills also mimic the woman's growing abdomen and her white skin; her condition mimics the snow-capped mountains over which the train in passing, and of which both the man and woman are largely trying to ignore. There is also a certain coldness of the mountainous terrain which mimics the icy nature of the relationship between the man and woman.
Traditionally, a "white elephant" is a possession that, while valuable, is not wanted by its owner. Today, we see in our culture "white elephant" gift exchanges, often between people who are just casual friends and do not want to buy gifts for one another--they are often popular at office parties. The fact that the young woman sees an image of white elephants in the hills is significant because she too is carrying something that is precious but still not wanted--a baby.
In the story "Hills Like White Elephants" two people are seen talking as they await the train. They seem to be having a simple discussion, but as one reads between the lines one learns that the discussion is about abortion. The woman and man are traveling for the woman to have an abortion. They have made many journeys and enjoyed their time together. She contemplates the idea of keeping the baby but the man reminds her that it is not what he wants in life and how happy they have been without the complication. I have often heard professors tell me that the hills like white elephnats are also like a baby bump and symbolize the baby in the woman's womb.