[think33]

A bitcoin faq would give you more details, but the short answer is that bitcoin is built on cryptography. Every transaction in the system is stored in a chain of blocks. These blocks are created whenever someone discovers the answer to a very hard mathematical problem. When they do this, the new block is created, and that block contains all the transactions that were done since the last block was created. To make the next block, you have to have the previous block, so the entire chain of blocks can be authenticated, thus the entire history of transactions can be authenticated.

As a reward for securing the system in this way, that is, providing a secure distributed transaction history, the miners are rewarded with some bitcoins whenever they discover a new answer and create a new block.

Thus they are providing the security of the system and as a reward are given bitcoins. To keep the rate of new blocks contstant, the difficulty of the mathematical problem is adjusted up and down. Over time, the number of bitcoins you get for finding a new solution will diminish to zero.

To keep miners finding new answers, even after the reward in BTC hits zero (in the year 2140) the system has transaction fees. These are an incentive to keep finding blocks, and the person who finds the next block gets the fees for the transactions that go into that block.

Since blocks are discovered once every 10 minutes, you'd get 10 minutes worth of fees for the whole system-- which could be quite a bit in the future.