Light with wavelengths from 400 to 700 nm is visible. Light of shorter wavelengths are ultraviolet, X-rays and gamma rays progressively. Longer wavelengths are infrared, microwaves and radio waves. Microwaves have wavelengths on the order of centimeters, while radio waves are on the order of several meters.
The reason people, like most animals, have vision in this narrow part of the spectrum has to do with the opacity of water. Note that in the graph below that light only penetrates water at these wavelengths. The scales are logarithmic.