For 8 bits/channel (as in JPGs for example), each R, G or B color is recorded on 8 bits, color value ranging from 0 to 255, i.e. 256 shades for red, 256 shades for green, 256 shades for blue. In total this gives 256x256x256 colors or 16 million colors.
In 16 bits there are 65536 shades for each R, G or B color. This gives 281,474 billion different colors.