'‘The’ and ‘a’ are … called the definite article (the) and the indefinite article (a, an). In modern grammar, both are called determiners.' (Language into Languages Teaching, University of Glasgow, Scottish Executive Education Department, 2001)
The definite article is the word 'the' in English.
In French, the definite article is 'le' if the noun is masculine and 'la' if the noun is feminine.
Both of these are shortened to 'l’ if the noun begins with a vowel, to make pronunciation easier.
'Le', 'la' and 'l’ all become 'les' if the noun is plural.
In French, you cannot use 'à' together with the definite article 'le' or 'les'. Instead, the two words contract to form 'au' ('à' + 'le') and 'aux' ('à' + 'les'), both meaning 'to the'.
Similarly, you cannot use de together with the definite article 'le' or 'les'. Instead, the two words contract to form 'du' ('de' + 'le') and 'des' ('de' + 'les'), both meaning 'of the'.
The indefinite article in English is 'a', 'an' or 'some'.
In French, the indefinite article is 'un' if the noun is masculine and 'une' if the noun is feminine.
'Un' and 'une' become 'des' if the noun is plural.
If there is an adjective, 'un beau jardin' becomes 'de beaux jardins' in the plural.
The article can be omitted in English. For example, we can say 'I love cakes'. In French, the article cannot normally be omitted. Therefore, if we wish to express in French the sentence 'I love cakes', we have to decide whether the speaker means 'I love (all) cakes' or 'I love (some) cakes'. If we agree that the statement is a general statement referring to 'all cakes', then in French we would use the definite article and the sentence becomes: 'J'adore les gâteaux'.
If we were to say: 'J’adore des gâteaux', it would mean that the speaker loves some, but not all, cakes.