One of innovations to come out of Bitcoin is the notion that every financial transaction that happens is recorded in a distributed public ledger. This ledger is called the “block chain”. Every bitcoin transaction that occurs, or has ever occurred, is recorded on the block chain. In addition the block chain is distributed by Bitcoin “nodes”. Nodes talk to each other (peer 2 peer) and that’s how the block chain is communicated throughout the bitcoin network (that will have to be another post). When you run a full bitcoin client on your computer, you become a node.
Collections of transactions are grouped together into “blocks”. And blocks are placed one after another into a long “chain” of blocks, thus the name “block chain”. If you try to alter a block then the cryptographic computations which make valid transactions would not work indicating that a block has been altered. Thus we are ensured that all the transactions are correct. As a new block is placed onto the chain a new computation is created (a hash) that depends on all previous blocks. This is why the blocks are chained together.
Since the block chain is available to everyone, anyone can check that a transaction has actually happened. Just like a regular financial ledger you can check the entire history of bitcoin transactions by looking in the block chain. The validity of transactions is ensured by the distributed network of bitcoin nodes and the cryptography used ensures that all copies of the block chain are valid. Purty cool ayeee!