From Wikibooks

A lot of people think that Issac Newton discovered his theory of gravity when he thought about why apples fall. In most versions, it is said that Newton was sleeping under a tree when an apple dropped on his head!

Through his thought on why apples fall, Newton found out that everything pulls everything else, as if everything, even you and me, are connected by invisible, and impossible to feel, strings. He decided to call this discovery gravity.

Before he came to that conclusion, Newton had to clear the way by thinking of an ideal environment, where he can work on his ideas without things from the real world affecting him. Although his ideal environment and his conclusions will be impossible in real life, he was able to create simple theories and best case versions of the events in the real world. He also found out that the real world follows his theories very closely, which made his models very important in predicting the real world.

The first idealisation he made was to think of everyday objects' weight and separating that from his ideal version, mass. Crucial in that is to also think in terms of forces, which is a push or a pull that acts only on mass. The relation between mass and weight is that weight is the force, usually of the Earth pulling on, on the mass of an object. In this way, he was able to think of a fixed amount of mass in any object which weights differently in different cases. For example, a person may weigh 60 pounds on a weighing machine on Earth, but that same person, with the same mass, would weigh 10 pounds on the Moon, even if it is the same weighing machine used.

Once that is done, Newton thought that all mass will naturally pull each other together, and that this pulling of masses towards each other follows some simple laws that can be easily represented in mathematics. One of such laws is that the more mass involved, the stronger is the gravitational force between the masses. Since you and me have much less mass than the Earth, the gravitational force between you and me is much less than the gravitational force between you and the Earth. In fact, no animal has yet to be able to feel another animal's gravitational pull on them! This just goes to show how heavy the Earth must be, if we can weigh it (and the Earth indeed has a huge amount of mass!)

From those, and more discoveries in the form of his famous 3 laws of motion (which will be discussed immediately later), he was able to create a nice, simple and accurate model of the universe we live in.