The definition of pure is pretty simple: "not mixed or adulterated with any other substance or material."
When it comes to purity of sound, we can extrapolate that to mean a pure signal without any added byproducts like distortion. Yet, I am not sure pure alone gives us what we believe we're looking for in performance.
For example, pure water is tasteless. If you don't believe me, try a swig of distilled water. It's the impurities in water that give it flavor. It's why you pay more for "spring" or mineral water. You're paying extra for their distortion.
Some of the lowest distortion audio products on the market are similarly unremarkable. I'll not be naming names or foisting my opinion on others, but let's just say a triple digit low distortion amplifier is not in itself a mark of great sound. Sometimes, quite the opposite.
Purity on its own is not always what we strive for. It is the balance of purity and flavor that makes for both great tasting water and great sounding audio equipment.
As we've seen so many times before, it's the balance of a product that defines its character.