Determiners are used before a noun to determine the character of the noun in particular, how definite or general a noun it is, and whether it is one or more than one. When you use a noun, you have the choice of using it in one of three possible states.
1. You can use the noun without any determiner at all.
in the singular, if it is a proper noun Boston is on the east coast.
in the singular, if it is an uncountable noun. I can hear music.
in the plural, if it is a countable noun. Tigers have black stripes.
When you use a plural countable noun without the article, you are seeing the noun in a general way – tigers in general.
2. You can use the noun with either of the articles, a or the:
use a with singular, countable nouns. I can see a car.
use the with singular countable nouns. I can see the car.
use the with plural countable nouns. I can see the cars.
use the with uncountable nouns. I can see the water.
The articles are the most common determiners in English. Their main job is to say whether the noun is definite or indefinite.
3. You can use the noun with one of the other determiners. This adds a further meaning to the noun. For example:
determiner adds the meaning of
my book possession also (our, his, her etc)
this book nearness to the speaker (also plural these)
that book distance from the speaker (also plural those)
some books quantity (also any)