What is the difference between a definite and an indefinite article?

Single Indefinite Article
Un/Une in French is in English what you would use as  a/an: 
a bottle = une bouteille
a mobile phone = un GSM 
an actress = une actrice
an actor = un acteur

Here you can see that for both a/an it is not just defined as a= un and an= une. It can be both.
Therefore for you to understand this, you have to know that in French they distinguish between the masculine and the feminine: 
Un = Masculine 
Une = Feminine
Because in English this does not exist, through practicing and reading, it will come naturally. 

Plural Indefinite Article
The plural of the indefinite is much simpler: in French you use des. Let's you want to say - I sell books. 
In French you would say: Je vends des livre(S) 
Un livre
Des livre(S) - add in the S because it is plural.


Definite article
The definite article in French is la, le and les. Its English translation is the. The definite article is similar to the indefinite in the sense that it distinguishes between masculine, feminie and plural. 
Masculine = Le
Feminine = La
Plural = Les

Another difference between English and French is that the English sometimes do not use an article, and the French always do. 

E.G. 
The rabbit is eating carrots = Le lapin mange des carrottes. 

When referring to an all of something in English, i.e. whales, rabbits, dogs, human etc. - in English, you do not use the the but in French you always do, e.g. 
Men have beards = Les hommes ont des barbes

Likewise, when the noun is referred to in a general sense, i.e. thai food. 
I like thai food - J'aime la cuisine chinoise
OR: I like football - J'aime le foot