in English what is the difference between the definite and in definite article?

a banana (you've never mentioned the banana before - indefinite.)

the banana (you've already mentioned it. We both know which banana you're talking about - definite)

The DEFINITE article (the) is used if you know which particular one you are talking about:

in the house, down the road, give me the paper, wash the cup, how is the dog? Would you like this orange? You know (DEFINITELY) which house, road, paper, cup, dog, orange, is being talked about.

The INDEFINITE article (a or an) is used to describe any of these things, not one particular one: I will be looking for a new house soon. Can I park on a road near you? Shall I buy a paper? Please give me a cup. I would like to have a dog. Would you like an orange [any one, out of this bowl of oranges]? You are not talking about (INDEFINITE) a particular house, road, paper, cup, dog as it hasn't been mentioned before.

Indefinite Articles—a, an

an—used before singular count nouns beginning with a vowel (a, e, i, o, u) or vowel sound:

an apple, an elephant, an issue, an orange

a—used before singular count nouns beginning with consonants (other than a, e, i, o, u):

a stamp, a desk, a TV, a cup, a book

Definite Article—the

Can be used before singular and plural, count and non-count nouns

Definite = the

Indefinite = a, an

They have different usages.

A cat sat on a mat

(means any cat, or one of several sits on any, or one of several, mat)

A cat sat on the mat

(means any cat, or one of several sits on a particular mat)

The cat sat on the mat

(means a particular cat, sits on a particular mat)

The cat sat on a mat

(means a particular cat, sits on any mat)

As with all rules there are plenty of exceptions mostly idioms, "On the road" for example simply means travelling and hence no particular road. "I am going to the theatre" does not imply any particular theatre, it means you are going to a theatre to see a play.