The Equivalence Principle
For instance, standing on the ground on Earth is the same as being on a platform in space accelerating at 9.8 m/s^2. (If you doubt it, think about being in an elevator. As the elevator is accelerating up, you can feel it pushing up on you. If you stand on a scale while this happens, it will read you gaining weight. The acceleration due to gravity and due to the elevator are impossible to tell apart).
This concept is very simple, and it makes sense. It also has dramatic consequences for the world in which we live.
One of these can be called “falling photons”. Think about the room accelerating at 9.8m/s^2, and think about shining a laser pointer across that room. What will happen? As the photons travel, the room will be accelerating upward, which means that the photons appear (to someone in the room) to arc down. Because of the equivalence principle, we know that this happens in gravitational fields too.
This effect was one of the first predictions of general relativity to be confirmed. The position of light from distant stars was measured during an eclipse and found to be different from measurements made while the stars were in plain view.
There are many other spectacular consequences of general relativity, most of which have been confirmed: time is slower in stronger gravitational fields; light is red-shifted (its frequency shortened) when traveling against a gravitational field; and black holes exist, objects so massive that past a certain point (the event horizon), not even light can escape their gravity.
Einstein figured this all out by simply thinking about gravity and the equivalence principle. The math gets very complicated, but the core concept is so simple it can be entirely explained in one sentence: gravitational fields are equivalent to accelerating reference frames. That’s good physics.