Well, you know how in physics, there's net motion? Like, if you are walking south at 3 kph on a bus that's moving 2 kph north, your net motion is 1 kph south? It's kind of like that; the speed of light itself doesn't behave this way (it doesn't net with the motion of its source), but its wavelengths are affected, so when an object is moving away from us, the wavelength of the light being emitted is stretched into a longer wavelength, so the image appears to have more red light (as it has a longer wavelength).