Blockchain is shared, trusted, public ledger of transactions, that everyone can inspect but which no single user controls. It is a cryptographed, secure, tamper resistant distributed database. It solves a complex mathematical problem to exist. A blockchain is the perfect place to store value, identities, agreements, propery rights, credentials, etc. Once you put something like a bitcoin into it, it will stay there forever. It is decentralized, disintermediated, cheap and censorship resistant. Applications of Blockchain: Bitcoin (cryptocurrency), Namecoin (wants to replace the entire DNS system of the internet), or Blocksign (non disclosure agreements at very low costs  of only a few cents), Ethereum (Turing complete virtual Machine where you can run any kind of smart contract); Any centralized service like Ebay, Dropbox can potentially be built in a decentralized way using blockchain technology, considerably lowering transaction costs.