Of a "something", Why does "Of" can be used here and how to use it?

Definition #10 in Merriam Webster gives this:

10 — used as a function word to indicate a characteristic or distinctive quality or possession: a woman of courage

So of can be used to describe the attributes of a person, similar to how it can be used to describe the attributes or components of an object - "heart of gold", "nerves of steel", etc.

In a comment John Lawler wrote:

Of is the default preposition used to link two nouns together, when one is felt to be needed. It can indicate possession, partitive, or some other property; or it can be governed by a particular noun, or a particular nominalization. For instance, the shooting of the hunters can mean either that the hunters shot, or that they were shot. But the shooting of the hunters by the soldiers is unambiguous, because grammar: when nominalizing a transitive clause like the soldiers shot the hunters, the subject takes by and the object takes of, no matter what.