Ethereum is an open source project created by Vitalik Buterin in 2015. Ether is the token that fuels the Ethereum blockchain, an incentive ensuring that developers write quality applications and that the network remains healthy.
Ethereum made it possible for programmers to create smart contracts, otherwise called self-executing contracts, blockchain contracts, or digital contracts. In this format, contracts can be converted to computer code, stored and replicated on the system and supervised by the network of computers that run the blockchain.
This innovation moved the story of blockchain forward significantly, and is partially why Ether - the token of the Ethereum project - has also risen in prominence and recognition.