Bitcoin was the first true cryptocurrency and has been in circulation since 2009. Ethereum is a far more recent development, going live in 2015.
In the time between Bitcoin and Ethereums release, lots of other cryptocurrencies emerged. Mostly, however, they were limited to trying to improve on aspects of Bitcoins performance for example, increasing speed of transactions or improving the security or anonymity of transactions.
Ethereum is certainly faster than Bitcoin with transactions typically settling in seconds, rather than minutes. But it also takes things further. While still blockchain based, and operating as a store of value, its fans and evangelists see it as a platform for distributed computing, which comes with its own built-in currency, called Ether.
While the Bitcoin blockchain can simply be pictured as a database of accounts (or wallets) with an amount of currency stored in each, the Ethereum network blockchain is a more sophisticated construction, capable of storing computer code applications that can use the CPU power going into the network to execute.
The currency Ether represents this CPU power so the idea is that Ether will be bought and sold by businesses, governments or individuals to allow them to tap into the vast, distributed resources of the Ethereum network to run their own apps.
The first of these applications are known as smart contracts. This is a way of automating contracts and agreements so they will execute when consensus says that conditions have been filled. Though simple, their uses are potentially widespread such as enabling payment systems which will release funds on completion of work, or authorizing the transfer of ownership of good when payment has been made.
The Ethereum network also allows the creation of other cryptocurrencies, or tokens, using the same protocol as Ether but distributed on different blockchains, which can be public or private. This means they can be created by organizations to represent shares, voting rights or as means of proving identity or authorization credentials.