The purpose of Ethereum is to create a new protocol for creating decentralized applications, which provides a different set of trade-offs for a wide range of decentralized applications. (Ethereum Foundation)
'Decentralized digital currency' has been around for decades, with several proposals to create money through solving computational puzzles and consensus, but the concept has not been implemented in practice until 2009 by Satoshi Nakamoto's 'Bitcoin’.
Ethereum aims to provide a fully-fledged programming language for the creation of smart contracts. Proof of work is an algorithm that solves the problem of allowing free entry into the consensus process and preventing sybil attacks. Proof of stake is an alternative to proof of work, which uses currency as a voting mechanism. (ETH Foundation)