I read:

Suddenly – boink! -an apple hits him on the head. “Aha!” he shouts, or perhaps, “Eureka!” In a flash he understands that the very same force that brought the apple crashing toward the ground also keeps the moon falling toward the Earth and the Earth falling toward the sun: gravity

Now this story is not litterally true. It is written though that Newton sat in the garde where he spent his his childhood and saw an apple falling. He pondered why apples don't fall sideways but straight down instead.

How did this lead him to his laws? He imagined the apple being the moon that fell. And because of the Earth's curvature it would fall forever, so orbiting. But what is the connection with his universal law of gravitatio?