RRHODY wrote:"Moore's Law to roll on for another decade". Retrieved 2011-11-27. "Moore also affirmed he never said transistor count would double every 18 months, as is commonly said. Initially, he said transistors on a chip would double every year. He then recalibrated it to every five years in 1975. David House, an Intel executive at the time, noted that the changes would cause computer performance to double every 18 months."
Double the amount of transistors on a given cheap in principles mean double the amount of calculations that the chip can do, so that means double the performance. Of course there are a lot of technical difficulties involved in getting the chip to work than just doubling the number of transistor in it, and there is advancement made in what one can do with a given number of transistors.
But then, Moore's Law isn't backed by exact science, and it isn't something precisely stated nor is it something that can be proved mathematically. It's simply a statement describing how the semiconductor industry have been evolving. There is no need to take it too seriously, but it's always a good starting point to predict what's to come.