The definite article (the) modifies a noun that describes a particular thing. The indefinite article (a or an) modifies a noun that describes a generality. Compare the following:
An apple a day is good for your health. (general)
The apple in my hand comes from Prince Edward County. (particular)
A degree or diploma is a formula for success. (general; there are many degrees and many formulas for success)
E = mc² is the formula that made Einstein famous. (a particular formula)
1. The definite article (the), meaning ONLY ONE, modifies a noun that describes a particular person, place, or thing:
Elizabeth II is the queen of the United Kingdom. (There is only one queen of the United Kingdom and only one United Kingdom.)
The sun is the centre of our solar system. (There is only one sun in our solar system, and it only has one centre.)
2. The indefinite article (a or an), meaning ONE OF MANY, appears before a singular noun or adjective:
She is a scientist.
It is a warm day.
Life is a mystery.
That is a beautiful haircut.
Idiomatically, a may also have the meaning of “one.” Note that we rarely use “one” to modify a singular noun; a is customary, e.g., There is a mosquito in this room.
3. No article precedes a plural countable noun or an uncountable noun. When an article does not precede a noun, as in the examples below, we refer to it as zero (Ø) article:
Ø Men are different from Ø women.
Ø Nature is an interesting subject to study.
They are Ø friends of mine.
Ø Elephants are large.
Ø Money is useful for a good life.