Both the cat and dog have a poor color vision. This is because, unlike the human who have three types of cones, cats and dogs have only two types of cones. http://en.wikipedia.org/wiki/Cat#Senses has more information.
There can't be any explanation for this because nobody can see what dogs or cats can see. But what I can see is that they both can see color because I taught my cat and dog to do tricks based on colors but I don't know how their brain works so. I hope this helps.