Rather than being divided into different bands, visible light is divided into colors. The slight differences in the wavelengths of visible waves determine which color that the light is. Visible light is the "smallest" range of wavelengths of the seven main sections (logarithmically speaking) but it makes up everything we see.
Above: The division of visible light into a spectrum of colors. At the edges of the scale are near ultraviolet (the top) and near infrared (the bottom). The discovery of light as a composition of colors may have come in Isaac Newton's time (c. 1665), when the prism revealed sunlight as made up of light on many different wavelengths.
The prism is able to split visible light into its components because there are slight differences in the speeds of light through glass. Higher wavelengths are faster and have greater refraction angles, causing them to bend more and therefore appear at the bottom of the rainbow shown above. Red and other long wavelengths travel slower and refract at a smaller angle, causing them to be at the "top" of the rainbow above. Real rainbows work in a similar way, when water droplets disperse sunlight into the visible spectrum. This also proves that sunlight has many different wavelengths of light, by no means limited to visible light.
Visible, or optical astronomy, is by far the oldest type, and has been going on since antiquity. Only recently have observations in other parts of the spectrum expanded our knowledge of the heavens.
Sources: http://www.windows2universe.org/sun/spectrum/multispectral_sun_overview.html, http://www.juliantrubin.com/bigten/lightexperiments.html, http://en.wikipedia.org/wiki/Optical_astronomy
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