Briefly, it can be explained by a realistic painting that goes beyond photo realism. This is what the word means to me:
When we look at something we have to decide where to focus or gaze – if you look at a doll, the sourroundings and the background gradually gets blurry. It is the same think if you take a photo of a doll, you have to focus your camera on a certain point because you cannot get the photo completely sharp everywhere. Taking photos is a compromise when it comes to blurryness (we talked about that on the photo course), but also in other aspects like shading, colors, moving objects etc. When you paint on the other hand, you can decide to make the painting sharp with lots of details and colors throughout the whole painting if you want to. The painting gets even more realistic than the reality as seen through our eyes or a camera lens, amazing hu! Someone who paints photo-realistically on the other hand, would follow the original photo slavically.
What I love about hyperrealism is that you can push the boundaries of photo realism. You are no slave under the rules of photography. You can use your imagination and artistic freedom, make up shades and details which weren't there from the beginning. You can combine elements from different photos or from your own mind to create a painting as long as it looks real (which is what I do).
A parenthesis: In philosophy, hyperrealism refers to realism and the technological advancement. The mind cannot always distinguish between fantasy and reality (also think about video games). The reality we perceive (the hyper reality) might not be the same thing as the "real" reality.