It's pretty rare for a short story to go viral these days. It's not catchy enough. It's not a meme. Where are the pictures? Well, there is one horrifying picture illustrating Kristen Roupenian's New Yorker story "Cat Person" of two mouths kissing, but that's probably not why it's so popular.
The story itself is pretty simple. It's about a girl named Margot, who is 20, meeting a guy named Robert, who ends up being 34. The two meet at her job, flirt, have one terrible date and bad sex, and then part. The tale is told from Margot's perspective, and shows the confusion of being a young women trying to figure out men. At a certain point, it's very clear that Margot doesn't want to go through with having sex, but she does anyway, not knowing how to extricate herself from the situation.