Think of a blockchain like linked lists. The linked lists exist on the network and is peer to peer, so there is no central server that stores the data.

Whenever a new transaction is made, in the case of Bitcoin, a new node is created and joined to the linked list.

The bitcoin blockchain is limited in the sense that you can only buy / sell bitcoin. Ethereum is another up and coming blockchain that allows you to write smart contracts (contracts that enforce themselves). There is a whole community of developers working on developing decentralized applications for Ethereum blockchain now.

Come join us over at /r/ethereum