Pigment is the substance or powder that makes up the color of a paint. Pigments are either organic (derived from plant or animal sources, e.g. ivory black, indigo) or inorganic (derived from salts or metallic oxides e.g. ocher, cobalt blue).
Manufacturers give their colors different trade names, so if you're buying a new brand and are unsure whether you've got the right color, you can check by looking at on the tube label what pigment(s) that color is made from.
Pigments also vary in price. Paints are usually classified into series, indicated by a number on the tube, which cost increasingly more as the pigment becomes more expensive. So, for example, in Winsor & Newton oils, bright red is series one, cadmium red is series four, and carmine is series 6.