Bitcoin is a digital currency that operates independently of banks and governments.
Bitcoins derive value in the same way every other currency does. People are prepared to exchange bitcoins for money through exchanges and people are prepared to sell goods and services and be paid in Bitcoin. Simply stated, Bitcoins have value because people are prepared to give them value
Bitcoins are transferred directly from person to person via the Internet (or phone network) without going through a bank or clearinghouse. As soon as the transaction is verified by the Bitcoin network, the transfer is complete – takes maybe 10 minutes in my experience
This video does a very good job explaining the basics. Look out for the following things:
How Bitcoin are stored
How Bitcoin are created (called mining)
How a Bitcoin transaction works
How you can exchange Bitcoin for other currencies
Where you can use Bitcoin – buying computer games or videos; paying for a Dell computer; Buying stuff at Overstock; making donations and more
How you could Bitcoin to be paid in your business
Since this video was created a few things have evolved. Mining is now a much more complicated process requiring lots of computing power and cheap electricity. There are many more exchanges and more currencies can be traded for Bitcoin. Many more businesses are accepting Bitcoin.