Bitcoins are a bit like the Internet. Or, rather, the Internet as it was in the mid ‘90s: something strange, coming out of geekdom into mainstream perception, greeted by puzzlement over how it works, why it works and why anyone would think it’s useful.
A common analogy for Bitcoins is gold: like gold, they have value only because people want them, the supply is limited, more Bitcoins are created only by ‘mining’ for them and the difficulty in mining grows as they are mined. But rather than being stored in underground vaults Bitcoins are simply entries in a notional ledger held across many computers around the world.
The actual mining of Bitcoins is by a purely mathematical process. A useful analogy is with the search for prime numbers: it used to be fairly easy to find the small ones (Eratothenes in Ancient Greece produced the first algorithm for finding them). But as they were found it got harder to find the larger ones. Nowadays researchers use advanced high-performance computers to find them and their achievements are noted by the mathematical community (for example, the University of Tennessee maintains a list of the highest 5000).
For Bitcoins the search is not actually for prime numbers but to find a sequence of data (called a ‘block’) that produces a particular pattern when the Bitcoin ‘hash’ algorithm is applied to the data. When a match occurs the miner obtains a bounty of Bitcoins (and also a fee if that block was used to certify a transaction). The size of the bounty reduces as Bitcoins around the world are mined.
The difficulty of the search is also increased so that it becomes computationally more difficult to find a match. These two effects…