Bitcoin's the first mainstream internet currency. We have dollars, pesos, yuan, and now Bitcoins. The system's brand new, which is why you're hearing about it now. It's snowballing right now; in a few years everyone will have heard of it. There's a few big advantages of using Bitcoins over Dollars.
First, Bitcoin is decentralized. There's no bank or government that's in charge of the system. Instead, Bitcoin users agree on a common set of rules, and thanks to open source programming and cryptography, the system is secure. This decentralization means that unlike previous digital currencies, there's no one in the middle - Digicash, EGold, Liberty Dollars all failed due to noncompliance or poor business management or whatever, but Bitcoin will exist as long as people use it.
Second, there's a limited supply of Bitcoins. A coke cost your grandma a nickel, but costs you a buck fifty, because the Federal Reserve keeps printing more money, making each dollar worth a bit less. No one can 'print more Bitcoins' - one bitcoin will always be the same slice of the Bitcoin pie. [There are 21 million Bitcoins, but, you can split them up - I can senddue to inflation you 0.0005 Bitcoins, etc.]
Third, it's a democratic system. Using Bitcoins is as simple as getting a Bitcoin receiving address and telling people the address. Any Bitcoins sent to that address are now yours. It's just as easy to start receiving Bitcoins as it is to send Bitcoins, but if you want to accept Visa, it's a lot more difficult than simply using your Visa on Amazon.com.
[How does it work?]
Every Bitcoin transaction, ever, is stored in something called the Blockchain. This is like an accounting ledger that tracks which addresses are authorized to spend Bitcoins. When Alice's address sends Bob's address a bitcoin, this shows up in the block chain, at which point Bob is now the owner of the bitcoin. If Alice tries to send that same bitcoin to Carol, Carol's Bitcoin software will check the blockchain, and notice that she's no longer authorized to spend it, and reject the transaction.
[Who makes Bitcoins? How are they created?]
Right now there are 6 million bitcoins. They're generated at a predictable rate, as rewards for "miners" processing transactions for the network. This keeps everything secure - the more miners there are, the harder it is to attack the network. There is a competitive market to earn these coins; since they're in high demand. Anyone can use their computer to try and mine Bitcoins, but practically speaking, you need a high-end ATI graphics card to see much profit. The total computing power of the Bitcoin network is bigger than Folding@Home.