A blockchain is a peer to peer tool that works something like an open ledger. Every participant in a certain network has access to the whole history of every "transaction"- whether it be financial as in the case of Bitcoin, or also general information.
A distributed hash table (DHT) is a class of a decentralized distributed system that provides a lookup service similar to a hash table. Any participating node can efficiently retrieve the value associated with a given key. wikipedia
A block chain is a transaction database shared by all nodes participating in a system.
Blockchains have many potential appplications, but the most appealing is in security. According to Satoshi Nakamoto's calculations, it is almost impossible to forge a blockchain transaction once the history has passed a certain threshhold of difficulty, because the computer power required to attack the system would have to be more than the combined computer power of every node in the network.
Blockchain uses-cases - letstalkpayments.com