A smutty story, as in Teenagers love to tell dirty jokes. The use of dirty in the sense of “obscene” or “indecent” dates from the late 1500s, but its application to a joke began only in the 20th century. The same sense also appears in such expressions as dirty book, for a pornographic book;
dirty old man, for a middle-aged or elderly lecher; and
dirty word or
talk dirty, for a lewd, offensive expression or sexually explicit conversation.