And the next step would be to allow algorithms to have bank accounts, earn money for their work and then be charged, prosecuted and put in "jail" for X number of CPU cycles.
I'm pretty technically literate, but I have to admit I'm at a complete loss as to why this project matters (let alone what it does). Could you enlighten me?
Let me try.
The Ethereum vision encompasses three components: P2P messaging, a file distribution layer and Blockchains. I described them in more detail here: https://www.reddit.com/r/ethereum/comments/3npsoz/ethereum_i... In practice, this is actually more complex, but should suffice as an introduction.
The Ethereum developers are mostly focused on the Blockchain component. On-chain accounts can be associated with program code and state, the environment specifies a turing complete virtual machine, called Ethereum Virtual Machine (EVM). Transactions can call these programs (also called "smart contracts") and contracts can call other contracts as well. To avoid infinite loops, every execution step in the EVM incurs a fee ("gas cost") that is collected by the miner of the new block that include the transaction. If a transaction does not supply enough gas (paid in Ether, the networks currency), the fees are collected anyway and all changes are undone. The validity of the program state is guaranteed with a consensus algorithm. It is replicated across all nodes. So if you want to censor the program, you have to attack the entire network. This makes them reasonably independent of human control and thus allows them to control arbitrary state, including the networks currency.
But how can the contract communicate with the rest of the world? It can only do so using transactions. For example, it could incentivise transactions that supply it with information, or could use other contracts to schedule micropayments to some service.
Contracts could also be used to reference content addressed data (have a look at ipfs.io, these are basically the other two components) and thereby act as a (domain) name system.
All in all, this decentralises storage, state and communication and is the most futuristic thing I know of. It took me weeks to understand how these components relate to each other, but it was worth it.