The auditory nerve helps transmit sound signals from the inner ear to the brain. More precisely, the hearing-related portion is called the cochlear nerve, which carries electrical impulses from the cochlea into the brainstem.
Sound begins as pressure waves that vibrate structures in the outer and middle ear. Inside the cochlea, the organ of Corti and its hair cells convert those mechanical vibrations into neural signals. Fibers of the cochlear nerve then carry those signals to the cochlear nuclei, the first major processing station in the brainstem.
The term "auditory nerve" is commonly used for the cochlear nerve, but it is also sometimes used more broadly. The cochlear nerve is one division of the vestibulocochlear nerve, also called cranial nerve VIII. The other division, the vestibular nerve, carries information about balance and spatial orientation.
A common mix-up is to describe the nerve as creating hearing by itself. It transmits coded neural information; the brain processes those signals through several relay stations before sound becomes a conscious perception in the auditory cortex.