Guanciale is pork jowl: the cheek (guancia in Italian) of the pig, rubbed in salt and pepper and cured for a few weeks. It is not smoked, it has a stronger flavor than pancetta but it is more delicate in texture.
Guanciale is traditionally used in Roman dishes (or recipes from Latium region in general) such as amatriciana and carbonara. Purists and Romans insist on using it in their recipes, claiming it is essential for the perfect turn-out of the dish. However, since guanciale is not to be found everwhere that easily, even here in Italy, you can use pancetta (cured bacon, the not-smoked kind, called pancetta dolce) instead.