A craving is an intense desire for something really particular. If you have a craving for pickled herring, a tuna sandwich just won't do. Must. Have. Pickled. Herring.
Craving is the noun that comes from the verb crave, which comes from the Old English word crafian, meaning "to demand, beg." When we talk about cravings, it's almost like the body and not the mind that is demanding something. Pregnant women famously have crazy cravings, sending their partners to the store in the middle of the night for pickles or toffee. Some people have cravings for power or fame: the desire is so strong they can't let it go.