Ethereum is a decentralized platform that runs smart contracts: applications that run exactly as programmed without any possibility of downtime, censorship, fraud or third party interference. In the Ethereum protocol and blockchain there is a price for each operation. The general idea is, in order to have things transferred or executed by the network, you have to consume or burn Gas. The cryptocurrency is called Ether and is used to pay for computation time and for transaction fees.
If you want to earn block rewards from the network, you can join the network as a miner. Follow the link for a guide on how to mine Ethereum on a Windows Pc. The much easier but a bit more expensive way is to buy an Ethereum mining contract.
Ethereum is how the Internet was supposed to work. As long as you have enough funds to pay for your code to be run by the network, your contacts will always be up and running.
It was crowdfunded during August 2014 by fans all around the world. It is developed and maintained by ETHDEV with contributions from great minds across the globe. There is also an Ethereum foundation and there are multiple startups working with the Ethereum blockchain.
Ethereum is currently on the "Homestead" stage and all its related software is still considered Beta until the release of the next stage "Metropolis".
If you are looking for a GUI interface for your wallet, try the Ethereum Wallet DApp. It's still in beta so be careful when you use it.