The purpose of coating on a lens is to reduce reflections from the lens surface. They are applied as a single layer (single coating) or multiple layers (multicoating) that are a fraction of a wavelength of light thick. Coating eliminates flaws such as flare, ghosting, and low contrast caused by wayward light reflecting inside the lens.

The coating of the front lens element is critical to the performance of the whole lens assembly, and the colours of reflections seen in this front element indicate what kind of coating it has:
No coating:
bright white reflections from the glass
Single coating:
bright reflections of blue and amber
Multicoating:
reflections of many colors, especially green and purple