The cornea, the surface film of the eyeball, does not receive oxygen from the bloodstream like the rest of the body does. Instead, its oxygen comes from the air. The oxygen dissolves in the eye's tears and then diffuses along the cornea's surface.The opposite is also true. When the cornea needs to get rid of the waste product carbon dioxide, it releases the gas into the tear film, which then evaporates. You can reference more professional information in this page: http://about.daysoftcontactlenses.com/oxygen-and-your-eyes.aspx?ln=1
The cornea is unusual in that it is transparent - it has to be otherwise light could not enter the eye! The tissues that make up the cornea are able to maintain their transparency partly by not having blood vessels flowing through them. Without blood vessels the cornea must get it's Oxygen directly from the air. The Oxygen first dissolves in the tears and then diffuses throughout the cornea to keep it healthy. Equally important, the waste product of a healthy cornea is Carbon Dioxide which must be disposed of. This diffuses out of the cornea and into the atmosphere in the reverse process. Putting any contact lens into the eye will slow down or possibly stop this process. Without enough Oxygen the cornea will warp, become less transparent, less able to detect pain and can develop scars. Additionally, new blood vessels from the sclera (the white part of the eye) can grow into the cornea and cause further damage and scarring.
Every organ needs oxygen to run the cell processes with the energy that comes by oxidizing nutrients contained in the cells. To receive oxygen, they need to have access to blood. Since Cornea does not have any blood vessels, it cannot receive oxygen from blood. It absorbs oxygen directly from the air through diffusion. Oxygen gets dissolved in the tears and then diffuses across the cornea. However, the amount of diffused oxygen is so less that it is just enough for only the cornea cells. This can't be supplied to other parts of the body. And this is exactly the reason you would get yourself killed if you plug your nose and your mouth, expecting your eye would keep you alive by breathing in oxygen.