But what fully homomorphic encryption allows you to is to perform arbitrary computations on encrypted data.
So you send your encrypted data to a machine, it performs the computation, and sends it back to you still encrypted. Like the password list example you mentioned.
What is cool about this is that is solves the problem with privacy in cloud computing platforms. You don't expose your data.
NOTE: I'm not a cryptographer nor haven't read the article yet. Just writing what I can remember.