more info here:
Need to buy bitcoin with credit card first or "mine" bitcoins with a graphics card on your computer.
The computational "mining" process is used to keep the system secure and trustworthy. At present the combined processing power of bticoin miners is greater than the top 500 super computers - combined.
The system is set up as decentralised digital cash with all transactions being anonymous (to a point) and encrypted and verified by consensus. Transactions are irrevocable.
The system has been designed with the intended use as a global currency. There are no central banks and almost no limits to this currency.
I have "mined" 1 bitcoin in the last week with my computer which is somewhere between $15-30 USD (it is a very volatile currency at present).