The idea that dogs only see the world in black, white and shades of gray is a common misconception. What’s true, though, is that like most mammals, dogs only have two types of color receptors (commonly called “cones”) in their eyes, unlike humans, who have three.
Each of these cones is sensitive to a different wavelength (i.e. color) of light. By detecting different quantities of each wavelength and combining them, our three cones can transmit various signals for all the hues of the color wheel, the same way the three primary colors can be mixed in different amounts to do the same.