Final answer:
The orbicularis oculi is the circular muscle in the eye socket responsible for closing the eyes, distinct from the extraocular muscles which move the eyeball.
Step-by-step explanation:
The ring muscle of the eye socket that enables you to close your eyes is the orbicularis oculi. This muscle is one of the muscles that contribute to facial expressions and is responsible for closing the eyelids. It is different from the extraocular muscles which are responsible for moving the eyeball and are located in the orbit, the bony socket that houses the eyeball.
The orbicularis oculi muscle acts like a drawstring that when contracted, causes the eyelids to come closer together and seal shut. It functions in concert with other muscles like the levator palpebrae superioris, which is responsible for lifting the upper eyelid. Understanding this helps in diagnostics related to eye movement and eyelid function during physical examinations.