What exactly is a?

Answer 1

The word 'a/an' is called a determiner. It is placed before a specific noun to indicate it. It is called an 'indefinite article', usually preceding the initial occurrence of a noun. 'The' is a 'definite article' preceding nouns which are already introduced/familiar or assuming focus.

Compare:

"A man walked into the room."

"The man walked into a room."

In the first example, the man is introduced (preceded by the indefinite article), but we are presumably acquainted/familiar with 'the' room (definite article). In the second example, the man is definite, while the room is indefinite or as yet unknown.

"A hero took the prize" assumes we are familiar with the prize, and the 'hero' is a relative unknown. "The hero took a prize" assumes we are familiar with the hero. "The hero took the prize" assumes we are familiar with (or at least focused upon) each item (the hero and the prize). "A hero took a prize" is decidedly indefinite - we are not yet aware of who the hero is, or what his prize was.