Edit: I phrased that wrong. How do you usefully query other user's data with only your keys?
The use case - any private data which you'd like to encrypt on the server while preserving ability to search. Medical records, financial data, emails are some examples.
Easier to say what this database is not for. Big data applications where you need to use a significant portion of data in the db (like 10%) in map-reduce queries is probably not what ZeroDB would be practical for.
The final outstanding question I have though is: How do you deal with data you aren't the owner of? Is this strictly targeted at scenarios where you are the sole owner?
The other is when the owner of the data is some group (like JP Chase). In this case we can have server-side quotas for handling cases when one or several clients are compromised. So, in this case it's more about distributing trust