That’s perm as in permanent wave, which is what these cats appear to have. While the American Wirehair has a wavy but somewhat stiff coat, the fur of La Perm is curly but soft. (As with the Wirehair, a genetic mutation caused this.)
The curly hair extends only up to the neck; the hair on the head looks like that of an American Shorthair. (This looks either odd or appealing, depending on your point of view.) Curiously, La Perm kittens are often bald at birth, but in a few weeks they begin growing their curly coats.