You can check you color contacts and then you will find that there is a clear hole in the center for your pupil. Usually we will not see the color unless the contacts slide over our pupil. So that they will not change the color of other objects or affects their vision.
Color contact lenses cover the iris with a new color. But in the center of the contacts it is transparent. You can see the outside through this small hole clearly. There are two kinds of color contact lenses. They are enhancement tints and opaque colors. Both of them work with the same theory.