Simple version:Ethereum is a an enormously large computer network made of many computers throughout the world that check each other's results. Anyone in the world can run programs on the system, paying only for what they use.
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Less simple version: A unique developer platform that makes it very simple to build decentralized applications.
Ethereum is a decentralized platform and protocol that runs smart contracts: applications that run precisely as programmed without any possibility of downtime, fraud, censorship, or third party interference.
These applications run on a custom built blockchain, which is an enormously powerful shared global infrastructure that can move value around seamlessly and represent the true ownership of property. This configuration enables developers to create markets, move funds in specific accordance with instructions given long in the past (like a futures contract or will), store registries of debts or promises, and numerous other things that have not been created yet, all without counterparty risk or a middle man.
The Ethereum project was bootstraped via an ether (see What is Ether?) pre-sale during August 2014 by people from all around the world. It is developed by the Ethereum Foundation which is a Swiss nonprofit, with contributions from great minds across the globe.
Applications built with Ethereum do not cover all uses, but rather have special properties that make them unique as follows:
- Ethereum applications will always execute the code the application says it will. There is no "security through obscurity." There is no need to trust anything or anyone, because you can check the application code yourself.
- Ethereum applications are 100% and always and available. There is no downtime and the applications are guaranteed to be available in the future.
- Ethereum applications are extremely resistant to many types of attacks including DDoS or Denial of Service attacks which are rendered moot.
In the past, building decentralized applications mandated a detailed background in cryptography and mathematics, etc. Ethereum simplifies this protocol by making decentralize applications accessible to web developers.
There are many use cases of ethereum, of course or favorite is in the world of online gaming including poker, casino, sportsbook wagering, slots, blackjack, dice, craps and more, but developers can now also create apps that can be accessed by everyone, without restriction. The services would be traditionally owned and distributed by the Facebooks and the Googles of the world, but now can easily be developed by anyone and used by everyone. Reputation, identity, online communications and payment processing can now be all handled by the public domain.