Determiners are used with nouns to clarify the noun. They are used:
to define something or someone
The girl in the red hat.
The dog with the long tail.
to state the amount of people, things or other nouns
There are four people in the room.
There are a lot of toys on the floor.
to state possession
I like my car.
That is my sisters new dress.
to state something or someone is specific
I want the blue pen. I do not want the black pen.
We live in the big house at the end of the block.
to state how things or people are distributed
The dogs each get two cups of food.
There are more people that live in the city.
to state the difference between nouns
Do you want the green car or the white car?
Do you want the brown dog or the black dog?
to state someone or something is not specific
I need a blue pen. I do not care which blue pen.
I want some cake. I do not care which cake.