Light waves are actually vibrations of electric and magnetic fields, so they are part of the electromagnetic (EM) radiation spectrum. The light from the sun contains many colours of the spectrum. Although we cannot see all wavelengths with just our eyes alone, there are devices that can help fill in the gaps a bit. Each colour has its own wavelength properties, and the eye can interpret them with special receptors.
Each colour that the human eye can see has a different wavelength. Red has a long, wide wavelength and vibrates at 700 nanometres. Violet has thin, sharp wavelengths that vibrate at around 400 nanometres. The colour of an object that you look at is actually just the reflection of that colour while the others are absorbed into the material.
White light from the sun contains all colours and can be broken into distinguishable colours with a crystal prism. Rainbows are water vapour that light hits and breaks into separate colours.
You interpret light with the cone receptors in the retina at the back of your eye. Black and white are interpreted by the rod receptors in the retina. There are far more cone receptors in the retina, which is why you see colours clearer and better than you see black and white at nighttime. The blotchiness and tiny spots that you see at night with shades of grey are due to the lower number of rods and the space between the rod receptors that is occupied by the cone receptors.
Visible light is the light waves that we can distinguish with our eyes alone. There are several other wavelengths that we cannot see with just our eyes, but machines can detects some of these wavelengths. Infrared light waves are just out of our scope of vision. These are used for heating and thermal radiation. Microwave light waves are farther from our visual capacity and have long wavelengths. Microwave wavelengths work well for radars as they can penetrate through haze, rain, clouds and smoke.