Thanks for the info. Sounds interesting.
Here's my own explanation: bitcoin was invented in late 2008 (and launched in early 2009) by an anonymous cryptographer who went by the name Satoshi Nakamoto. It exists in the form of a ledger distributed amongst thousands of computers (miners), who share in updating the ledger and keeping it in sync.
Every 10 minutes (on average) a new block of transactions are added, and a miner is rewarded with a set amount of bitcoins (the reward halves every 4 years). Hence the term "blockchain" for the ledger.
Each block is cryptographically sealed to the previous blocks, such that, one accepted, no one can create an alternate blockchain that will be accepted.
The ledger records bitcoin ownership based on public keys, which are generated from private keys held by each bitcoin owner. You can share your public keys freely, as they can only be used to deposit bitcoin, not to send it to someone else. (For example, one of my keys is 19pMAfnS1prHg34k4ZQHKJrmMPkuqbXDoe if anyone is feeling generous :-)
Once it comes time to use your bitcoin, your bitcoin wallet provides a cryptographic hash of the transaction using your private key, proving you are the true owner of the public key in question. Your transaction is broadcast to the network and is added to the next block for a trivial fee to the miners (less than 3 cents at this writing, and you can sometimes do it free, especially if you are in no hurry). The miners are thus paid in block rewards and transaction fees, and in return they provide security to the bitcoin network, making it realistically impossible for any one party to corrupt the blockchain.
(OK, I assumed you were a _really_ bright 6 year old... maybe you should just start with Piggycoin instead! :-)