Bitcoins are best explained within this video.
To summarize: The beauty of Bitcoins are that no third party need be used or trusted since the entire digital currency runs on a peer to peer, decentralized network of computers. The encryption used to keep your transactions and currency safe is open-source and highly regarded and reviewed. You can transfer them from person to person over the internet which means you can use them pretty much anywhere to purchase anything without limit and no third party entity can freeze or hold your accounts.
So basically, it’s a revolutionary digital currency that could change the way we do business forever.