Ethereum is a system on the Internet where people can make self-executing contracts (called Smart Contracts). Such contracts will run without any downtime, fraud, control or interference from a third party. Ether is the currency used to facilitate these contracts, as well as to pay people (miners) who provide computation power to run them
As an example, assume a smart contract for earthquake insurance. The blockchain can contain measurable parameters such as earthquake magnitude. When there's an insured event, the input conditions of a smart contract will be changed accordingly. As a result, the claims process will be triggered immediately, and the financial payout can be delivered to a customer without any delays.
Ethereum was proposed in late 2013 by Vitalik Buterin, a cryptocurrency researcher and programmer. A large number of people donated money to support the development of the system. The system came online in mid 2015.