Of commonly introduces prepositional phrases which are complements of nouns, creating the pattern: noun + of + noun. This pattern is very common, especially to indicate different parts, pieces, amounts and groups:
Lima is the capital of Peru.
Twenty-four-hour TV news makes sure we all know the main events of the day.
Would you like some more pieces of toast?
We also commonly use of as a preposition after different adjectives (afraid of, generous of, proud of) and verbs (approve of, dream of, think of):
I never thought she could take a flight on her own at her age. I feel very proud of her.
Best of luck with the interview tomorrow. We’ll be thinking of you.
We use the structure determiner + of + noun in expressions of quantity:
Most of the new workers in the country are from Turkey.
Some of my best friends are computer scientists.
Of is optional with all, both, half except before the object pronouns me, you, it, him, her, us, them:
Both (of) the finance ministers have decided to resign.