Richness is a quality or characteristic, either of having a lot of money or of being plentiful. The richness of exotic bird life in Hawaii may be much more appealing to you than the richness of your wealthy neighbors.
When you use the noun richness to talk about an abundance of something, you're emphasizing how luxurious or bountiful it is. And if you mention the richness of a meal or a dessert, you're talking about its delicious, fatty, and filling nature: "The richness of this chocolate mousse is off the charts!" Sometimes richness also means "intensity," as in the richness of the deep blue sky.