Visible spectrum
Light with wavelengths from approximately 400 to 700 nm is visible to human eyes. Light of shorter wavelengths are called ultraviolet, X-rays and gamma rays progressively. Longer wavelengths are called infrared, microwaves and radio waves. Microwaves have wavelengths on the order of centimeters, while radio waves are on the order of meters.
The reason humans have vision in this narrow part of the spectrum is presumably related to the fact that the peak of the power spectrum of light from the sun is in that region. (Perhaps nocturnal animals tend toward a slightly different range -- I don't know.) Another factor that dictates the visible spectrum has to do with the opacity of water. According to the graph below, light only penetrates sea water easily in a narrow band of wavelengths that corresponds rather closely to the visible range. Note that the scales in the graph are logarithmic; outside the the visible range, the absorption quickly becomes many thousand times stronger. It would be interesting to speculate on whether this results from our visual system having evolved in water; or whether (my guess) it is because absorption of other wavelengths within the liquid (approximately sea water) of the eye make it easier to make a large and sensitive eye at the visual wavelengths. (Some creatures, e.g. bees, are known to see ultraviolet light; but they have much smaller eyes which would be less affected by the absorption.)