In short and simple terms, the phrase "nice richness" means something that has a good and valuable quality or abundance.
Sentences with «nice richness»
not too spicy, but a nice richness and real depth of flavour. (deliciouslyella.com)
I like to add some unflavored gelatin (softened in water) about an hour befor my Pot Roast is ready.It give a nice richness to the sauce. (sippitysup.com)
The sour cream adds a nice richness and tang, and the buttermilk adds additional zing. (davidlebovitz.com)