There was a BBC radio program a few weeks ago on the Blockchain called FutureProofing. The blockchain is a clever bit of applied encryption that let's people keep an accurate "ledger" of different types of transactions, a ledger that is open, distributed and easy to verify as being true. Its most famous application just now, and the reason it was invented, is its use by bitcoin, the electronic currency.
The Economist magazine has a better explanation of the blockchain and why it's so interesting :
All sorts of companies and public bodies suffer from hard-to-maintain and often incompatible databases and the high transaction costs of getting them to talk to each other. This is the problem Ethereum, arguably the most ambitious distributed-ledger project, wants to solve. The brainchild of Vitalik Buterin, a 21-year-old Canadian programming prodigy, Ethereum’s distributed ledger can deal with more data than bitcoin’s can. And it comes with a programming language that allows users to write more sophisticated smart contracts, thus creating invoices that pay themselves when a shipment arrives or share certificates which automatically send their owners dividends if profits reach a certain level. Such cleverness, Mr Buterin hopes, will allow the formation of “decentralised autonomous organisations”—virtual companies that are basically just sets of rules running on Ethereum’s blockchain.