The curved shape of the eye combined with the way light refracts off that shape causes people to see things upside down. Brains visually processes the information so people "see" the image as right side up, according to PhysLink.com.
The best way to understand why eyes see this way is to look at a reflection on the inside of a spoon. The image seen there is upside down. This is because light reflects off the retinas, which are at the back of the eyes, explains Women's and Children's Health Network. The iris allows a certain amount of light into the eye and its lens changes shape to create a clear image for retinas to process. The retina uses cells called rods and cones to produce an image for the brain to process. Cones process color, while rods process blacks and whites. Together, they convert the picture into an electrical message the brain can then use.
This is made even more complicated by the fact a person has two eyes, and therefore two image inputs. PhysLink.com describes other processes the brain goes through to create an image people can understand. Along with flipping the image right side up, the brain combines the pictures received by each eye.