Light comes in different wavelengths. If you collect light in at least 3 different wavelengths, you have "color" as the human eye/brain knows it. If you want it to match what our eyes see, you collect light at the same three parts of the EM spectrum that the three different color sensors in our eye are sensitive to.

The reason for them giving off different amounts of light in different wavelengths is that different molecules and atoms emit, absorb, and scatter light differently. Things of different temperatures also give off different wavelengths of light. All of which can be collected and assigned to one of the axes of the color space of an image.