From a computer science perspective, Ethereum is a deterministic but practically unbounded state machine, consisting of a globally accessible singleton state and a virtual machine that applies changes to that state.
From a more practical perspective, Ethereum is an open source, globally decentralized computing infrastructure that executes programs called Smart Contracts. It uses a blockchain to synchronize and store the system's state changes, along with a cryptocurrency called ether to meter and constrain execution resource costs.
The Ethereum platform enables developers to build powerful decentralized applications with built-in economic functions. While providing high availability, auditability, transparency, and neutrality, it also reduces or eliminates censorship and reduces certain counterparty risks.
Many people will come to Ethereum with some prior experience of cryptocurrencies, specifically Bitcoin. Ethereum shares many common elements with other open blockchains: a peer-to-peer network connecting participants, a Byzantine fault-tolerant consensus algorithm for synchronization of state updates (a proof-of-work blockchain), the use of cryptographic primitives such as digital signatures and hashes, and a digital currency(ether).
Yet in many ways, both the purpose and construction of Ethereum are strikingly different from those of the open blockchains that preceded it, including Bitcoin.
Ethereum's purpose is not primarily to be a digital currency payment network. While the digital currency ether is both integral to and necessary for the operation of Ethereum, ether is intended as a utility currency to pay for use of the Ethereum platform.
Unlike Bitcoin, which has a very limited scripting language, Ethereum is designed to be a general-purpose programmable blockchain that runs a virtual machine capable of executing code of arbitrary and unbounded complexity. Where Bitcoin's script language is, intentionally, constrained to simple true/false evaluation of spending conditions, Ethereum's language is Turing complete, meaning that Ethereum can straightforwardly function as a general-purpose computer.
The components of an open, public blockchain are (usually):