So...Lore-wise, what exactly is Azurite?

As an aside, this is where we get the name of the color cerulean blue. The cheap beads you see are made of this stuff.

I think we all knew since Bestiary that GGG loves their Pliny. :)

A few people in here are saying it is what makes Niko mad, but that's not the azurerite. What is making him mad is the sulphite, that he mines for fuel. As for the purpose of azurite, other than a game mechanic not really sure. It's just good shit that Niko needs for upgrades so you can delve further and find more good loots.