Color (also colour, from celare, "to cover") is the perceived visual quality of light that's associated with its wavelength/frequency (or mixture of several); for example red, blue and yellow are colors. Electromagnetic waves with wavelength from about 380 to 750 nm (about 400 to 790 THz) form the visible spectrum, i.e. waves our eyes can see -- combining such waves with different intensities and letting them fall on the retina of our eyes gives rise to the perception of color in our brain. There is a hugely deep color theory concerned with the concept of color (its definition, description, reproduction, psychological effect etc.). Needless to say colors are extremely important in anything related to visual information such as art, computer graphics, astrophysics, various visualizations or just everyday perception of our world. Color support is sometimes used as the opposite of systems that are extremely limited in the number of colors they can handle, which may be called monochromatic, 1bit (distinguishing only two colors), black&white or grayscale. Color can be seen to be in the same relation to sight as pitch is to hearing.
How many colors are there? The number of colors humans can distinguish is of course individual (color blindness makes people see fewer colors but there are also conditions that make one see more colors) but various sources state we are able to distinguish millions or even over 10 million different colors on average. In computer technology we talk about color depth which says the number of bits we use to represent color -- the more bits, the more colors we can represent. 24 bits are nowadays mostly used to record color (8 bits for each red, green and blue component, so called true color), which allows for 16777216 distinct colors, though even something like 16 bits (65536 colors) is mostly enough for many use cases. Some advanced systems however support many more colors than true color, especially extremely bright and dim ones -- see HDR.
What gives physical objects its color? Most everyday objects get its color from reflecting only specific parts of the white light (usually sunlight), while absorbing the opposite part of the spectrum, i.e. for example a white object reflects all incoming light, a black one absorbs all incoming light (that's why black things get hot in sunlight), a red one reflects the red light and absorbs the rest etc. This is determined by the qualities of the object's surface, such as the structure of its atoms or its microscopic geometry.
This is actually a non-trivial question, or rather there exist many varying definitions of it and furthermore it is a matter of subjective experience, perception of colors may differ between people. When asking what color really is, consider the following:
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