Ethereum is a decentralized platform that runs smart contracts. People can make deals on this system. Ether is the coin used on the Ethereum system. These apps run on a custom built blockchain, an enormously powerful shared global infrastructure that can move value around and represent the ownership of property.
This enables developers to create markets, store registries of debts or premises, move funds in accordance with instructions given long in the past (like a will or a futures contract) and many other things that have not been invented yet, all without a middleman or counterparty risk.