A block chain is a transaction database shared by all nodes participating in a system. Block chain technology was popularised by the cryptographic currency Bitcoin.
From Bitcoin by Analogy
Approximately six times per hour, a new group of accepted transactions, a block, is created, added to the block chain, and quickly published to all nodes.
Apart from financial transactions it as a number of applications. See Block Chain Projects.
YOUTUBE QzDO44oZWtE The mechanics of a bitcoin transaction block chain, which is a construct that is generated by bitcoin miners and functions as a global ledger for recording and validating bitcoins - khanacademy.org
Here I collect some examples of projects using Block Chain Technology.
A proof-of-work (POW) system (or Protocol, or Function) is an economic measure to deter Denial of Service Attacks and other service abuses such as Spam on a network by requiring some work from the service requester, usually meaning processing time by a computer.
In the case of cryptocurrency Proof-of-stake is a method of securing a network and achieving distributed consensus through requesting users to show ownership of a certain amount of currency.
A blockchain is a peer to peer tool that works something like an open ledger. Every participant in a certain network had access to the whole history of every "transaction"- whether it be financial as in the case of Bitcoin, or also general information.