The article is a structural word specifying the noun.

§1. Functions of Articles with Common Nouns. A (the indefinite article)

Is used with

Countable nouns	Uncountable nouns
the nominating function sg	The aspective function
- when we wish to name an object (a thing, a person, an abstract notion) which is usually new to the hearer. He gave her a cigarette. (the indefinite article originates from the numeral one that is why it implies the idea of oneness (единичность) and is used only before nouns in the singular)	The indefinite article brings out a special aspect of the notion expressed by the noun A dull burning anger rose in his chest. (= in this case the noun is qualified by an attribute which also brings out a special aspect - черта).

what is the main difference between the definite and indefinite articles?

When the speaker uses the indefinite article, he just names an object which is usually new to the hearer. So the indefinite article is often used to introduce a new element in the sentence. Since the new element is, as a rule, important and attracts attention, the noun with the indefinite article frequently becomes the centre of communication and is marked by strong stress (THE RHEME).

e.g. I think he is a stupid fellow.

Presently the Browns arrived. They brought with them a small child, a governess and a dog.

The table was covered with a white cloth.

In contrast to this, the definite article usually indicates that a definite object is meant and that it is not new to the hearer and so the noun is not the centre of communication (THE THEME):

e.g. I bought a book yesterday. – Вчера я купил книгу

(we learn what object was bought yesterday. So a book is the new element in the sentence)

I bought the book yesterday – Я купил книгу вчера.

(the hearer learns when the book was bought (he already knows that the speaker bought a book). In this case the book is not the centre of communication.)

In the Russian language which has no article, the centre of communication is usually marked by word-order and also stress.

В комнату вбежал мальчик. A boy rushed into the room.

Мальчик вбежал в комнату. The boy rushed into the room.

Их послали в мае на конференцию . They were sent to a conference in May.

Их послали на конференцию в мае. They were sent to the conference in May.

Тне (the definite article)

Is used with

Countable nouns	Uncountable nouns
1) the individualizing function (sg& pl ) = the noun denotes a particular object, thing, person, group of objects as distinct from the others. (the definite article serves to single out an object/objects from all other objects of the same class) Margot took up the telephone.	The restricting function = the definite article restricts the material denoted by a concrete uncountable noun to a definite quantity, portion, locality. The leather of the gloves was perfect.
2) the generic function = the noun becomes a composite image (собирательный образ) of the class The tiger has always had the reputation of a man-eater. When was the telephone invented?