Next-Generation Smart Contract and Decentralized Application Platform
Ethereum is a platform and a programming language that makes it possible for any developer to build and publish next-generation distributed applications.
Ethereum can be used to codify, decentralize, secure and trade just about anything: voting, domain names, financial exchanges, crowdfunding, etc.
Ethereum borrows the concept of decentralized consensus that makes cryptocurrencies so resilient, yet makes it trivial to build on its foundation.
A World Computer
In a technical sense, Ethereum is a "world computer". Harking back to the days of the mainframe.
An Internet Service Platform
In a more practical sense, Ethereum is an internet service platform for guaranteed computation.
Opt-in Social Contracts
At a more abstract level, it is a facility for enabling smart organization, in the sense of groups of entities working together for a particular cause.
You may ask, "why would anyone use such a system?" and again there are many reasons. The main reason is because it makes what you want to do cheaper and easier. This statement needs to be broken down somewhat, which is what the following paragraphs explore.
Furthermore, as long as it is in demand, the Ethereum World Computer will always be there: it can't be shut down or turned off.
Ultimately, Ethereum could be used to run countries. Somewhere in between there are groups of people wanting to organize baby-sitting circles, film-making collectives, discussion groups, communal houses, etc, and they all have to decide the rules with which they will operate together.
Ethereum provides a platform on which rules can be defined and, to an ever increasing degree as technology improves, see enforced.
"It is very possible that ... one machine would suffice to solve all the problems ... of the whole [world]"
Sir Charles Darwin, 1946
"Technology gives us the facilities that lessen the barriers of time and distance - the telegraph and cable, the telephone, radio, and the rest."
Emily Greene Balch
"This is an era of organization"
Theodore Roosevelt, 1912