(from the Purdue OWL website https://owl.english.purdue.edu/owl/resource/540/1/)
What is an article? Basically, an article is an adjective. Like adjectives, articles modify nouns.
English has two articles: the and a/an. The is used to refer to specific or particular nouns; a/an is used to modify non-specific or non-particular nouns. We call the the definite article and a/an the indefinite article.
the = definite article
a/an = indefinite article
For example, if I say, "Let's read the book," I mean a specific book. If I say, "Let's read a book," I mean any book rather than a specific book.
Indefinite Articles: a and an
"A" and "an" signal that the noun modified is indefinite, referring to any member of a group. For example:
"My daughter really wants a dog for Christmas." This refers to any dog. We don't know which dog because we haven't found the dog yet.
"Somebody call a policeman!" This refers to any policeman. We don't need a specific policeman; we need any policeman who is available.
Remember, too, that in English, the indefinite articles are used to indicate membership in a group:
I am a teacher. (I am a member of a large group known as teachers.)
Brian is an Irishman. (Brian is a member of the people known as Irish.)
Seiko is a practicing Buddhist. (Seiko is a member of the group of people known as Buddhists.)
Definite Article: the
The definite article is used before singular and plural nouns when the noun is specific or particular. The signals that the noun is definite, that it refers to a particular member of a group. For example:
"The dog that bit me ran away." Here, we're talking about a specific dog, the dog that bit me.
"I was happy to see the policeman who saved my cat!" Here, we're talking about a particular policeman. Even if we don't know the policeman's name, it's still a particular policeman because it is the one who saved the cat.
Some common types of nouns that don't take an article are:
Names of languages and nationalities: Chinese, English, Spanish, Russian (unless you are referring to the population of the nation: "The Spanish are known for their warm hospitality.")
Names of sports: volleyball, hockey, baseball
Names of academic subjects: mathematics, biology, history, computer science