Ethereum
After Bitcoin was launched, people starting thinking of many other uses for blockchains besides just as a store of value. One of those people was Vitalik Buterin, a teenager in Canada who together with a team of collaborators came up with the idea of a multi-purpose blockchain called Ethereum.
Ethereum was designed to let anyone build arbitrary applications on the blockchain — if it can be written in code, it can be built on Ethereum. Because of this, Ethereum is often referred to as the World Computer.
You can think of Ethereum as a public App Store, where anyone in the world can upload an application that can then be used by anyone else.
Since this World Computer is public, you have to pay to operate it — if you are uploading an app, the cost of computing power to do so must be paid in Ethereum's native cryptocurrency, Ether (or ETH). If someone else wants to run that app, the same rule applies: they must pay the computing cost to run it in ETH.
If Bitcoin is digital gold, ETH is digital oil. Like oil, ETH can be used as fuel to power more economic activity. In oil's case, that activity is factories, cars, and cargo ships, and in ETH's case, it is decentralized internet applications.
This cost to execute applications in Ethereum is commonly referred to as gas. Similar to Uber surge pricing, when the Ethereum network is busy, the cost of gas rises, and when it's less busy it decreases.
Most people think of ETH (the cryptocurrency) when they think of Ethereum (the platform/app store). Hopefully the distinction between them is a bit more clear now, and you're starting to see that Ethereum is a lot more than just a cryptocurrency.
Here are a few resources to start understanding how Ethereum works.
If you are comfortable with a technical overview, definitely read the Ethereum Whitepaper — it explores the motivation of Ethereum using Bitcoin as a starting point. Ethereum Whitepaper