In a way, by using the three LEDs we are playing a trick on the eye. This same idea is used in TVs, where the LCD has red, green and blue color dots next to each other making up each pixel.
We can control the brightness of each of the red, green and blue parts of the LED separately, making it possible to mix any color we like.
Black is not so much a color as an absense of light. So the closest we can come to black with our LED is to turn off all three colors.