I would argue that Martha actually represents lots of things to Cross, and she acts as quite a complex symbol in this short story. Most of all, however, she clearly represents escapism. Cross is shown as a man who is under a lot of pressure and so having Martha's letters allows him to dream and to escape the responsibilities and role that he has been given and that oppress him so greatly. Note how this is presented in the following quote:
He would imagine romantic camping trips into the White Mountains in New Hampshire. He would sometimes taste the envelope flaps, knowing her tongue had been there.
Clearly Cross needs this escapism and the way that he invests so much time and mental energy into "pretending" and creating lavish fantasies of love between himself and Martha indicates how important escapism is for him. Of course, this is something that he comes to view as a dereliction of his duty, as he comes to believe that this daydreaming was responsible for the death of one of his men.