Moore's Law originated in a four page 1965 magazine article written by Gordon Moore, then at Fairchild Semiconductor and later one of the founders of Intel. In it he predicted that the number of components on a single integrated circuit would rise from the then current number of roughly two to the sixth power, to roughly two to the sixteenth power in the following ten years, i.e., the number of components would double every year. He based this on four empirical data points and one null data point, fitting a straight line on a graph plotting the log of the number of components on a single chip against a linear scale of calendar years. Intel later amended Moore's Law to say that the "number of transistors on a chip roughly doubles every two years".
Moore's law is rightly seen as the fundamental driver of the information technology revolution in our world over the last fifty years as doubling the number of transistors every so often has made our computers twice as powerful for the same price, doubled the amount of data they can store or display, made them twice as fast, made them smaller, made them cheaper and in general improved them in every possible way by a factor of two on a clockwork schedule.
But why does it happen? Automobiles have not obeyed Moore's Law, neither have batteries, nor clothing, nor food production, nor the level of political discourse. All but the last have demonstrably improved due to the influence of Moore's Law, but none have had the same relentless exponential improvements.
The most elegant explanation for what makes Moore's Law possible is that digital logic is all about an abstraction, and in fact a one-bit abstraction, a yes/no answer to a question, and that abstraction is independent of physical bulk.
In a world that consists entirely of piles of red sand and piles of green sand, the size of the piles is irrelevant. A pile is either red or green, and you can take away half the pile, and it is still either a pile of red sand or a pile of green sand. And you can take away another half, and another half, and so on, and still the abstraction is maintained. And repeated halving at a constant rate makes an exponential.
That is why Moore's Law works on digital technology, and doesn't work on technologies that require physical strength, or physical bulk, or must deliver certain amounts of energy. Digital technology uses physics to maintain an abstraction and nothing more.
Some caveats do apply:
1. In his short paper Moore expressed some doubt as to whether his prediction would hold for linear, rather than digital, integrated circuits as he pointed out that by their nature, "such elements require the storage of energy in a volume" and that the volume would necessarily be large.
2. It does matter when you get down to piles of sand with just one grain, and then technology has to shift and you need to use some new physical property to define the abstraction—such technology shifts have happened again and again, in the maintenance of Moore's Law over almost fifty years.
3. It does not explain the sociology of how Moore's Law is implemented and what determines the time constant of a doubling, but it does explain why exponentials are possible in this domain.