The state transition function defines how the state transitions from one block or one transaction to a new block. So your blockchains pretty much are the model, if you like, the computation model. There is some structured state or database or storage that sticks around between blocks and there is some code that tells you what the new storage is. It's as simple as that.
We finally sit down with Gavin to go through a bit of what Parity has been working on with Polkadot and Substrate. We talk about Polkadot early history and who was involved and where the idea spawned, up to coding practices and where Substrate became a thing.
If you want to know more, links below.