What is the main purpose of the Ethereum network?

Could you please elaborate on the core objective behind the establishment of the Ethereum network? I'm particularly interested in understanding its primary function and how it differs from other blockchain platforms. Could you also discuss its significance in the world of cryptocurrencies and finance, and any potential implications it might have for the future of digital transactions and decentralized applications? I'm keen to gain a deeper understanding of this fascinating technology and its potential impact on our financial ecosystem.