The mole on Miss Vashner's eyebrow is a key distinguishing feature of her physical description: the young man at the center of the story describes her as
A fair girl, of medium height and slender, with reddish gold hair and a dark mole near her left eyebrow.
The mole is the only thing that sets Miss Vashner apart from any other medium-height young woman with light hair in New York. And this is the feature that allows us to know at the end of the story that Miss Vashner had indeed rented the room right before the young man and had committed suicide in it, for Mrs. Purdy says that
she'd a-been called handsome, as you say . . . but for that mole she had a-growin' by her left eyebrow.
The mole allows O. Henry to tell us the truth indirectly, without actually telling us; the reader has to connect the dots between the mole in the otherwise unremarkable description of Miss Vashner given to us by the young man, and the poor woman mentioned by Mrs. Purdy. And in the end, it is this connection that makes this story a tragedy in the eye of the reader, and that gives the suicide emotional weight.