The Benefits of Bitcoin
This purely electronic credit exchange system has various benefits, not least the fact that it is extremely secure, taking advantage of public and private key cryptography to indicate to the recipient of the Bitcoin payment that you are who you say you are, that the Bitcoin belongs to you and that the transaction is legitimate.
While there are questions over the handling of disputes over Bitcoin transactions (something that will need to be resolved if the payment system is to ever reach the same mainstream use as something like PayPal), this is a system that is held in high esteem by its proponents.
Bitcoins can be used for all manner of transactions, from ordering food and staying in hotels to web design services, hosting, music, clothes, books, art and much more. A quick browse through the Bitcoin wiki reveals hundreds of businesses that will accept this payment method in exchange for goods. Once several such transactions have completed, these businesses will then be able to see their Bitcoins in exchange for a national currency, such as the US dollar.
Ultimately, Bitcoin is an online payment method that while secure, isn't devoid of fraud. Any system of monetary exchange is going to find itself exploited, but one would hope that Bitcoin's reliance on a community time line of transactions could save it long term rather than see it consigned to history as soon as a better, more secure and completely fraud proof system is introduced.
For more information on Bitcoin and more detail on the use of cryptographic monetary transactions, see How To Turn Bitcoins into Real Currency.