There are two things at work that would make it a good idea for your body to close its eyes for sleep.
The first being that during the day we are constantly blinking to lubricate and moisten our eyes. At night, keeping your eyes closed protects them from drying out and getting irritation and from building up mucus in the eye ducts.
The second has to do with a chemical known as melatonin. Melatonin is dependent upon the light and dark rhythms around your body. When it is nighttime and the light around you begins to disappear, your body begins to produce melatonin which is a signal to your brain that it is time to sleep. The darker it is, the more melatonin your body will produce. Once it lightens again, your body stops producing melatonin and it signals your brain again that it is time to awaken.
It is best for your body to close its eyes so that they can sense as little light as possible, produce more melatonin and thereby convince your brain to sleep.