The RGB color beams produced by a CRT (a device that can generate an image on a phosphor screen by scanning three or more colored cathodes) are a bit tricky to understand, as is the phosphor itself. The CRT's three or more cathodes create different colored beams, which intersect in the phosphor. The phosphor converts the energy in the beam, which is usually ultraviolet, into the color that you see in the screen.
To understand how this works, consider the different colors of light coming out of a white light bulb. White light is a mix of all colors of light, including red, blue, and green. The different wavelengths in white light separate and travel at different speeds. Red light travels fastest, green light is slower and blue light travels slowest. These different wavelengths of light can be used to determine how a CRT can be scanned.
This is how a color television works. The cathode rays are scanned across the phosphor, converting the phosphor to the colors that you see on the screen. When you turn the power on to the television set, the cathode ray guns are energized. They are scanned across the screen and are converted into different colors by the phosphor on the screen.