I'm not sure specifically as there could be many short stories named 'the moustache'. It might be about a character with a moustache and the events or experiences related to him. Maybe it's about how his moustache affects his appearance, relationships or the way people perceive him.
Well, without having read the exact 'the moustache short story', it could potentially revolve around the significance of the moustache in a particular culture or time period. It might tell a story of a man who is judged based on his moustache, or perhaps it's a story where the moustache is a symbol of something, like masculinity, rebellion or a connection to a certain group.