Dr Gavin Wood, co-founder of Ethereum, released the first draft of his latest project, ‘Polkadot: Vision for a Heterogeneous Multi-Chain Framework’ in November 2016.
The project anticipates that there will eventually be a number of blockchains and that they will all need to communicate with each other and transfer value across chains. For example, a private blockchain operated by a consortium of energy supply companies many need to interact with a decentralised application running on the Ethereum blockchain, such as a peer to peer energy trading platform.
If we think of ‘Bitcoin as Blockchain Accounting’ and ‘Ethereum as Blockchain Computing’, we could think of Polkadot as ‘Blockchain Internet’.
It is complicated and it is not yet fully formed, but Gavin Wood gives an excellent explanation of Polkadot at this video. I suggest first that your read the draft paper which you can access here as this will make the video much easier to understand, particularly as he works his way through explaining the diagram on page 6 of the paper.