Ethereum is a technology that leverages a way to confidently know what transactions were conducted (a distributed ledger protected from tampering). In this way it is similar to Bitcoin, but it differs in that Ethereum was designed to enable smart contract execution. What this means is that not only can the Ethereum blockchain support the use of cryptocurrencies, but now applications can be written on top of this distributed ledger, and those applications can be written in ways that will automatically execute when certain criteria have been met.
Ethereum enables distributed applications, or Dapps.
The best way to examine what this can do for you is to dive in. Do that by creating a Coinbase account and transferring some funds there to purchase the Ether crypto currency. Then install MetaMask into your web browser to use as a Crypto wallet and transfer some of your Ether into that wallet.
But why do that? In part it is to prepare yourself for what is to come. This is clearly the wave of the future. But Ethereum can also enable you to make online purchases securely, reducing the chance of fraud again you while protecting your privacy. It can also enable you to enter into smart contracts with suppliers and can allow you to make investments in organizations where you can confidently know what your terms are. Additionally, it will enable you to write your own smart contracts and interact with others using your own smart distributed applications.
For a succinct overview on how Ethereum works see this short video: