A Blockchain is a form of distributed computing which runs a public ledger of monetary transactions, or other records. It first came into popular use with cryptocurrency, although other uses for this technology are now being found. Each update (new block) to the ledger is hashed along with the previous transaction and a nonce, and sent out to other nodes. They check to ensure that the new block is valid, then add it to their copies of the ledger.
Blockchain technology was perfected by a person (or persons) calling them self Satoshi Nakamoto. He devised a method to ensure a reliable transaction system, which did not permit double-spending (which can now only be accomplished if the blockchain allows changes to past or current updates). The result of this was Bitcoin. However, as Satoshi Nakamoto noted in his whitepaper, this system works, but only as long as the blockchain is composed of a majority of honest nodes. If more than half of the computing power running the blockchain agrees on a fraudulent update, the blockchain can be subverted to believe this falsified log. This is known as a "51% attack," because at least 51% of the blockchain's computing power is maliciously validating fraudulent blocks. It is very difficult for even a 51% attack to change past transactions, but it can falsify new ones. The difficulty and cost of such at attach increases proportionally to the number of honest nodes in a blockchain, meaning that there is safety in numbers.