Color is visualized by light reflecting off of rods and cones within the structure of our eyes. We sometimes see colors differently due to the effectiveness of these rods and cones, which is why people describe colors differently.
1 Additional Answer
The light receptors at the back of our eyes are cones and rods. While the rods allow us to see in dim light, the cones allow us to see color. You can find more information here: http://www.hhmi.org/senses/b110.html