Before any explanation, we should know that there are three primary colours viz., red, blue and green. All these three colours combine to form white and absence of these form black colour. This same theory applies to surfaces or light of various colours.
Any body or surface appears of a particular color because it reflects light of that wavelength. For example leaves appear green because the pigment chlorophyll present in it reflects green wavelength of light and absorbs the rest of the wavelength.
Similarly If a body appears white it means it is not absorbing any of the light and reflects all the incident wavelengths.Since white light is a combination of all wavelengths of light.
A black body or surface in a similar manner absorbs all the wave lengths of lights incident on it and reflects none. So the absence of any wavelength in the reflected light make it appear black.