Bitcoin is a form of digital currency, created and held entirely electronically.
A key difference between Bitcoin and a "fiat" currency like the US Dollar, is Bitcoin is decentralized. No bank or government controls it, and its value is determined by the free market, much like shares of stock are.
Bitcoin has many advantages over the current financial system. Unlike a credit or debit payment that can take days to process, a Bitcoin payment is fully settled in an hour or less. Bitcoin also has much lower fees for sending it, since there is far less overhead and red tape. It doesn't have the security risks of a credit card, since you don't need to give out any account info to use it. A Bitcoin payment is a "push" transaction, similar to an email. A Bitcoin payment can also be sent anywhere in the world very easily.
In a world that is becoming a lot more digital, more global, and much more connected by the Internet, Bitcoin just makes a lot of sense.