The main innovation that Ethereum brought over Bitcoin is the idea of the smart contract. Smart contracts are sets of instructions that allow programmers to create new and interesting applications built on top of the underlying blockchain. This is an advancement over the design of Bitcoin, which only allowed for user-to-user financial transactions to take place on its network.
Smart contracts are a type of account on the Ethereum blockchain. This means that they have a balance and can send transactions across the network. However, they are not directly controlled by a user, but are instead published to run independently on the network by those who program them. Users can interact with smart contracts by submitting transactions that trigger certain desirable events in the contract.
Perhaps the greatest advantage of smart contracts is their automatic execution without the need for intermediaries. This is on top of the trustless and transparent nature of their underlying blockchain network. Previously, whenever consumers had to interact with financial institutions or companies, they would heavily rely on the reputation of such bodies to conduct business in honourable ways. Smart contracts on the other hand are completely open to scrutiny by anyone who can access the public network (transparent). They can also be relied on to execute their code no matter what, i.e. without the need for any middlemen or managers (trustless).