mass noun and count noun

mass noun
a noun (as sand or water) that characteristically denotes in many languages a homogeneous substance or a concept without subdivisions and that in English is preceded in indefinite singular constructions by some rather than a or an
[M-W's Dictionary]

count noun
a noun (as bean or sheet) that forms a plural and is used with a numeral, with words such as many or few, or with the indefinite article a or an
[M-W's Dictionary]

1: What is an indefinite singular construction?
2: What is an indefinite plural construction?
3: What is an definite singular construction?
4: What is an definite plural construction?
5: As name suggests a count noun is countable, then how can one use indefinite article a or an with it?

1. a car, a pencil, an elephant, a man, a person, a concept;
sand, water, meat, butter, milk, wine;
faith, sincerity, persistence, knowledge
2. cars, pencils, elephants, men, people, concepts;
some cars, some pencils, some elephants, some people, some concepts

3.  the car, the pencil, the elephant, the man, the person, the concept;
the sand, the water, the meat, the butter, the milk, the wine;
the faith, the sincerity, the persistence, the knowledge
4.  the cars, the pencils, the elephants, the men, the people, the concepts

5.

... a count noun is countable, then how can one use [the] indefinite article a or an with it?

It's easy.  You just did it yourself when you wrote a count noun.    Countable doesn't mean definite.  Countable doesn't mean indefinite either.  If a noun is countable, it means that you can count whatever it is that is represented by that noun.

CJ

Thanks a lot for answering my questions.

Best wishes, Jackson