The thing is, that the comet is not merely reflecting sunlight, as the moon does. It's also acting as a very large fluorescent light bulb as the gas boiling off it is stimulated to emit visible light by the sun's ultraviolet. While the comet itself is tiny, astronomically speaking, the light-emitting tail may be millions of mile long.

See: http://www.solarviews.com/eng/comet.htm