There are two types of cells in the retina that receive light: rods and cones. Rods are for sensing motion and work best in low light conditions. All mammals, including people, have more rods than cones. Cone cells are adapted for vision in brighter light and can detect different colors. Humans have three types of cones. Dogs have two types of cones. Evidence suggests that the dog has vision similar to a human who is red-green colorblind. Cats have three types of cones, like people, but do not have exactly the same color vision as we do.
Dogs and cats appear to respond to blue and yellow best, and seem to have more trouble with green and red. What appears red to us is simply dark to the dog and cat, and green light is almost indistinguishable from white (a shade of gray). Colors that would appear very rich to us are probably more pastel-like to the cat. The cat would see a green, grassy lawn as a whitish lawn, and a green rosebush as a whitish bush with dark flowers.