A. Article
1. An article is a word as a determiner that indicates definiteness of a noun as general (indefinite article: ‘a’ or ‘an’) or specific (definite article: ‘the’).

B. An Indefinite Article 'a' and 'an' is a determiner that introduces a noun phrase and implies to a general or non-specific thing, or to introduce new concept. (e.g. I bought a book; Jon went to a public school). 
1. to introduce a noun phrase and implies that a thing referred to is general or non-specific. (e.g. I am going to buy a book for you.)
2. used to introduce new concepts into a discourse. (e.g. A story is a promise letter for my future life.)
3. Generally, we use “an” (not “a”) before a/e/i/o/u (e.g. a watch, an idea)

C. A Definite Article 'the' is a determiner and used in front of a noun that introduces a noun phrase and implies to one particular thing (specific), or is common knowledge, or is about to be defined. (e.g. the book on the table). The definite article can be used with singular, plural, or uncountable nouns. Compare with indefinite article.
1. to introduces a noun phrase and implies that the thing has already been mentioned (e.g. When we were on holidays, we stayed at a hotel. Sometimes we ate at the hotel and sometimes we went to a restaurant.)
2. common knowledge (e.g. Life can be very hard for the lazy people. The art is long, life is short, opportunity fleeting, experiment dangerous, judgment difficult.)
3. thinking of a specific thing (e.g. Hundreds of people have complained to the company about new politics.)
4. know exactly what we are referring to. (e.g. I am going to the church. (our church))