Put simply, the colour gamut of human eyes is all the colours we can distinguish. It is said that animals not only see colours differently, but also see colours outside the gamut of human vision.
The colour gamut of a camera is the colours it can 'see' and record. As digital camera sensors are responsive to some infra red (IR) and some ultra violet (UV) light which human eyes cannot detect, a camera's gamut is not the same as human vision.
The colour gamut of a printer is determined by the colour chemistry of the dyes or pigments in the inks it uses, and the colour and absorbency properties of the paper that is printed on.
The gamut of a computer screen is determined by properties of the phosphors (in an old CRT screen) or LEDs that are used as well as the basic calibration settings that determine the luminance and 'white point' of the screen.
Neither printers nor computer displays can produce the range of colours that a camera can capture, or the eye can see. What is important in managing a colour photography workflow, is that your camera is capable of capturing more colour than your printer can reproduce and both have bigger gamuts than your computer screen.