In 2015, Dr Gavin Wood, CTO of Ethereum, gave a presentation entitled "Ethereum for Dummies". 
This article contains my summary of his presentation. Times are approximate.
Main issue: "So now we've built it, what is it, exactly?"
Originally: Bitcoin-like thing with some features removed and some new layers / extensions (particularly in the internal scripting language). Goal: Abstraction platform for financial contracts on a blockchain.
- Bitcoin is crypto-finance.
- Finance is a subset of law.
- Ethereum is crypto-law?
For a long period, we didn't know exactly what it was.
- Answer: Ethereum is a computer.
-- Slow: Code runs 5-100x slower than natively compiled.
-- Expensive to use: Basic computation, memory, and storage costs are ~1950s levels.
-- Not always immediately decisive: Actions of last 60 seconds may be reorganised.
- Ethereum-the-computer has some interesting properties:
-- Truly global singleton: One computer for the entire planet, now and forever.
-- Cannot fail, be stopped, be censored: No authority, government or corporation behind it, resistant to attack.
-- Ubiquitous: Wherever there's Internet, there's Ethereum.
It's a computer that doesn't reside in any particular machine, and can't be turned off.
- More properties:
-- Natively multi-user: Has as many accounts as needed.
-- Natively object-oriented: Encapsulation enforced in "virtual silicon".
-- Verifiable & Auditable: All code in the computer is unalterable.
There aren't that many computers on which we can replay everything from the past and always be absolutely certain of getting the same result.
-- Atomicity: Entire operation runs or nothing does
-- Synchrony: No two operations can interfere with each other
-- Provenance: All messages (method calls) can be inspected to determine caller address.
- More guarantees:
-- Permanence: Objects' data are permanent
-- Immortality: Object can never be externally deleted - can only voluntarily commit suicide
-- Immutability: Object's code can never be changed
- What's the point of a World Computer?
-- Ethereum is an "Innovation Commons", compared to the walled garden of the server.
--- You don't need to think about signing partnership contracts in order to interoperate with another business (like e.g. Uber and AirBNB would have to do before making their systems work together). No need even to ask permission from the other party.
--- "this unleashes massive amounts of potential innovation from business"
- Obviously there is less privacy (the data is stored in many places), but you should think more carefully about what data you upload to it. Cf. False security of placing data on a third-party server and trusting it to keep that data safe.
- Authenticity: All interactions with the Global Computer are cryptographically signed: Unauthorised interactions are impossible.
- Ethereum is the first Decentralised Computer.
- Ethereum commoditises trust.
- We could call it "a platform for zero-trust computing".
-- For: autonomous trading, smart contracts, interoperable infrastructure, permissions management, trust webs...
- Ethereum could be the Court of the Internet.
-- Underpins, specifies and enforces dealings.
-- The Internet could have its own place to determine what is right or wrong. And perhaps arbitrate between two parties who are in conflict.
- Ethereum and crypto-law.
-- Ethereum is a decentralised legal system native to the Internet.
-- We can use blockchain to implement arbitrary social contracts without a central server.
- Ethereum and the Serverless Internet:
-- Pivotal in the (re-)decentralisation of the Internet.
-- We are in the "Post-Snowden Internet".