This may come off as a silly question and you may be wondering if your eyes actually breathe.
To answer that question we could say, somewhat_._ Your eyes don't breathe in the same sense as you do with your lungs, but your eyes do need oxygen just as every other organ and tissue in your body. You may already be aware that your lungs inhale oxygen and exhale carbon dioxide, that inhaled oxygen will be pumped throughout your entire body in the form of oxygenated blood, allowing your organs to function properly. Except, that blood isn't delivered everywhere where oxygen is needed.
If you look at your eyes in the mirror you will notice a few blood vessels in the white parts of your eyes (the sclera), but, there are no blood vessels in the cornea (the clear part of your eye). This is very intentional otherwise we wouldn't be able to see clearly if we had blood vessels blocking our lenses, but our cornea still needs oxygen to supply all the living cells inside of it. Without oxygen the cells wouldn't be able to survive or repair themselves, or even fight pathogens which could lead to swelling, cloudiness or infections.
Our eyes take oxygen directly from the air, the thin film of tears your eyes are always coated in (or should be) allows oxygen to dissolve into it, then diffuses directly into your cornea supplying all the cells. This is why it's not recommended to wear contact lenses for prolonged periods of time, outside of a few other reasons.
So if your eyes take oxygen directly from the air after dissolving in the liquid coating your eyes, how does this work while you sleep? Well, when you close your eyes the inner layer of your eyelid, containing blood vessels, releases small amounts of oxygen into your closed eye tear film allowing it to once more diffuse into the cornea. This process is basically the same as before but with a different source of oxygen, making it less efficient than taking oxygen directly from the air but it's enough to keep your eyes maintained throughout the night.
