Newton’s apple fell from the tree and after thumping the scientist on the head, fell benignly to the ground. If the same apple fell toward Einstein (and happened to have a little added atomic oomph), it could, according to special relativity, become infinitely massive, flattening not only the unfortunate Einstein as he sat bodhisattva-like beneath the tree, but also the Earth itself.
This doesn’t mean Newton was wrong—only, that his theories apply more accurately to things traveling at speeds that don’t approach the speed of light (from slow-moving atomic particles to city transit busses). The crucial postulate of Einstein’s theory is the idea that the speed of light is measured to be exactly the same no matter the motion of the observer.
If you think about it, this is a little weird: usually speed does depend on the motion of the observer—if you are driving down the highway, you will measure the relative speed of a bicyclist very differently than would a kid sitting at a roadside lemonade stand. Don’t worry—unless you, the bicyclist, or the kid is traveling near the speed of light, you can leave your intuitive understanding of this situation intact.
With the speed of light remaining constant (c=3x108 m/s), other terms in equations that include c must—sometimes counter intuitively—be variable. For example, Einstein’s now-accepted interpretation of the Lorentz transformation proves that time is variable, meaning that if a very, very fast spaceship returned to earth, the clocks on the ship would lag behind the time shown on Big Ben.
Special relativity also relates mass and energy as variables (E=mc^2), which explains nuclear power and explosions (generally, since c is a huge constant—especially c-squared—there’s a whole lot of energy trapped in a little bit of mass. When scientists found a way to liberate this energy, things went boom).
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