|English: Encrypted message authentication (Photo credit: Wikipedia)|
What does this mean for us? We can perform any mathematical circuit of functions on our encrypted, private data on untrusted systems (see: "The Cloud"), without ever exposing that encrypted data to untrusted users, servers or machines. Online banking, where you transfer/add/remove funds on an account without ever showing the account number? Check. Google Docs / text processing in the cloud without ever revealing what you are writing to the people who own those servers? Check.
The issues right now is that it takes a long time to generate keys and perform these functions. But to be able to live in a time where this was correctly implemented is mindblowing.