Ethereum is a world computer. As in, it acts like a single public computer that can perform computations for anyone who is willing to pay for them, but instead of this computer being run by a third party, it's run by the network as a whole.
This is useful for any situation where you would usually need a trusted third party to perform some computations or enforce one side of a bargain - for example ecommerce/escrow, trading, voting, bets, issuing stock/currency, plus other things that probably have not even been thought of yet.
I agree, it can be a pretty wishy-washy mission statement at times. But then again, so was the idea of a global communications network where anyone could communicate with everyone and publish their own content in the 1980s.