An identifier is that little word in front of a noun, often at the beginning of a sentence, that helps determine if the noun is someone or something specific or if it is general and therefore can apply to anyone or anything specific.
Note that my favorite sentence use a specific identifier:
The cat sat on the mat.
The sentence refers to one and only one cat*
We can alter the sentence in a variety of ways:
A cat sat on the mat.
The cat sat on a mat.
A cat sat on a mat.
And so on†.
The moment we need to know if a person, place, or thing is specific to one cat or possibly any cat, we change the identifier to reflect the reality.
* — A very specific cat, like Garfield or Bill the Cat, isn’t necessary as a definition of cat. It is meant to understand that a specific cat, though not what specific cat, is the subject of the sentence.
† — Actually, I think that’s the full list of variables for The cat sat on the mat.