Visible light is the same form of radiation as x-rays, radiowaves, microwaves etc- electromagnetic radiation (EMR). The frequency of the wave is what determines its wavelength and each type of EMR is associated with different ranges of wavelength. Visible light falls in ~400-700nm range, with violet/blue light at the lower end and red light at the upper end as you mentioned.
Waves of light do not inherently possess color. Color is a biological phenomenon. In humans, our visual systems have evolved to best detect EMR in the visible light range (hence the name). Cone cells in our retinas have special proteins called opsins that respond to specific wavelengths (frequencies) of light within visible range and each corresponds to a different spectrum of the visible range (ie blue, green, red). After a photon (light wave) of the correct frequency hits an opsin, it triggers a structural change that allows it to interact with neurons in the eye and transmit a signal to the occipital (visual) cortex of your brain. Our brains have evolved to associate ~400nm light as blue, ~500nm light as green and ~600nm light as red.
But we can distinguish ~1mil different colors of light instead of just blue green and red. The different colors we see are a result of mixed input from each of the different opsins/cones and the strength of those signals relative to one another. Black is the absence of color – black objects absorb most frequencies of light in the visible spectrum instead of getting reflected into our eyes. White objects reflect most frequencies of visible light and when those reflected waves hit our cones the combination is balanced out and we do not see color. This is why sunlight appears white but in a rainbow (where white light is refracted into narrower ranges of wavelength by water droplets in the air) we see several colors.
If you have a pocket microscope or a dslr camera, put it up against your TV or computer monitor and focus it. You should be able to see individual units (pixels) that contain red green and blue diodes. Instructions from the computer change the voltage applied to those diodes to change the mixture/intensity of each diode which changes the *perceived* color. A white screen will have equal intensity of each diode.
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