Determiners have two main functions: referring and quantifying.
Referring means showing us who or what the noun is pointing to or talking about. The most common types of determiners which we use for referring are articles, possessives and demonstratives:
It’s onthesofa. (the means the noun refers to something the speaker and listener both know or are familiar with)
Have you seenmyMP3 player anywhere?
Yes. It’s onthekitchen table. (my refers to something which belongs to the speaker; the refers to something the speaker and listener can both identify because they both know or share knowledge about it.)
Do you want this bag or are you going to put it in that box? (this refers to something near the speaker; that refers to something further away.)
Charles is looking for his dictionary. Have you got it? (his means the noun refers to something belonging to a male, in this case, Charles.)
‘Quantifying’ means showing how much of something there is, or how many:
Five people were arrested during an anti-war demonstration in London today.
There are some letters here for you. (some means a non-specific, small number or quantity of something.)
Do you have enough flour to make the bread. (enough means a quantity that is sufficient or adequate for something).