A color space is a set of colors also called gamut. The gamut of a monitor represents all the colors it is able to display. The gamut of a printer represents all the colors it is able to print.
There are 3 different color spaces:
L*a*b* is the largest color space, representing the set of colors that a human being can see. All other color spaces are smaller because technical limits keep devices from reproducing so many colors, for now at least.
CMYK is a subtractive (reflected light) color model using cyan, magenta, yellow and black inks in color printing. All colors start with white "paper", to which different color "inks" are added to absorb (subtract) light that is reflected.
RGB is a additive (projected light) color model to sense colors in digital cameras and to display colors on screens. All colors begin with black "darkness", to which different color "lights" are added to produce visible colors. RGB "maxes" at white, which is the equivalent of having all "lights" on at full brightness (red, green, blue).