Ethereum is crytpocurrency and a decentralized application platform. It is also, according to some, "the greatest technological advance since the creation of the Internet."
Ethereum was first described in a white paper by cryptocurrency researcher and programmer Vitalik Buterin, who argues that Bitcoin lacks an essential feature needed in a general-purpose payment system: he wants something like email for money. The system would be capable of moving value around as easily as we send emails today.
What is Ethereum?
Ethereum is a decentralized platform that runs smart contracts: applications that run exactly as programmed without any possibility of downtime, censorship, fraud or third party interference.
Ethereum can be used to codify, decentralize, secure and trade just about anything: voting, domain names, financial exchanges, crowdfunding and company governance among other things.  A Rootstock sidechain is also in the works for Bitcoin to allow similar functionality on the Bitcoin blockchain. 
Ethereum is a decentralized platform that runs smart contracts: applications that run exactly as programmed without any possibility of downtime, censorship, fraud or third party interference.  These smart contracts are based on blockchain technology which means they are transparent, secure and unhackable.  Smart contracts make it possible to create self-executing agreements that are immediately executed by the other parties in a transaction. The Ethereum Virtual Machine (EVM) automates the execution of these smart contracts and ensures they adhere to protocol rules.
Smart Contracts in Ethereum enable you to code your own contracts in Solidity, Serpent, LLL, etc.
Smart contract blockchains are needed but not sufficient. We need to work on a lot of smaller things that will make the technology usable for all kinds of applications, especially in the financial services area.
There are several ways in which smart contracts may be used in real life: - Custodianship for estate planning and asset management.
- Voting and consensus mechanisms.
- Contractual relationships between organisations and their suppliers, contractors, customers, etc., such as insurance contracts or employment contracts.
To understand what Ethereum is we need to realise that it's not a "one-size-fits-all" technology; the project was always meant to serve as a platform for other projects and applications that developers could build upon it.