What this means is that computer speed, storage capacity even pixels in digital cameras follow this exponential growth rate. It is hard to understand exponential growth rates. So much that even Alan Turing estimated that by the turn of the millennium, we would have computers with storage capacities of 10^9 (today's approximate to 128MB).
Although this is not a law of nature, rather an acute observation dating back to the invention of the integrated circuit in 1958. Moore's law has set the standards for industrial long-term planning. These days though it gets more and more difficult to follow so companies need to spend more and more money into R&D, to follow the harsh competition between them. At this point Moore's law becomes a self fulfilling prophecy; It lays the rule for the arms race in semiconductor industry competition. This is where Moore's second law (or Rock's Law) comes in.
The photo in this post is not inaccurate. Today's cell phones have more computing power than NASA had during 1969 when they sent Apollo 11, and the first man walked the Moon. Valentine's cards, those with the lame songs playing when you open them, have a microchip that has more power than all the Allied Forces of 1945. Today's Playstation 3 costing 300$, has the power of a military supercomputer of 1997, which cost millions of dollars.
But there are limits to how much can be fitted on to chips effectively, and Dr Moore predicts that his law has about 10 to 20 years before a fundamental limit is reached. Also as computing power becomes more and more cheap for the consumer, the R&D, testing and fabrication process of said integrated cicuits also doubles with every generation of chips. This means that computer power will stop growing exponentially until other methods of computing are developed, like quantum computing or DNA computing.
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