A story does not have to have a meaning. The purpose of a short story is to convey an emotional effect. What is important is the feeling that is left with the reader upon finishing the story. Most readers must feel terribly sorry for the pregnant girl because she wants to keep the baby growing inside her and also because she is coming to the realization that the man's feelings for her are not as strong or as sincere as she had supposed. She loves him more than he loves her. The reader might end up with the feeling that what is true in the relationship between this couple is unfortunately true of many relationships between men and women. The fact that they are in a foreign country and she doesn't even speak the language makes her seem even more pitiful.
The man and the woman are speaking about abortion.
This is the primary theme, but there are others: tension, isolation, and disconnection.
As the couple wait for the train, the woman gazes at the snow topped mountain.
"They look like white elephants," she said.
"I've never seen one," the man drank his beer.
"No you wouldn't have."
All of the themes of the story are hinted at here. The woman may be thinking of the mountains and her own body, which will soon be as swollen as the hills. The fact that they are cold and snow-capped may bespeak the isolation and "coldness" of her partner who does not want the pregnancy.
Additionally, there is symbolism present in calling anything a "white elephant." A white elephant is something that is not wanted:
"It's really an awfully simple operation, Jig," the man said, "It's not really an operation at all."
The fact that the couple refuse to directly say to one another the words "pregnancy" or "abortion," is akin to the adage, "the elephant in the room," which means something everyone knows but refuses to acknowledge. Even at the end, when there has been no resolution, the woman continues to ignore the (literally) growing problem. The story closes on these lines:
"Do you feel better?" he asked.
"I feel fine," she said. "There's nothing wrong with me. I feel fine."