We use Clojure mostly for its "Minority Report"-like interactive development in situations that require 'semi-automatic programming' (data inspection, admin tasks, API exploration, scrapers, etc.). We have also used Clojure successfully to build some components of our stack very quickly and reliably, in the backend and the frontend.
We use Clojure in several places, most often as a wrapper around other libraries and frameworks (e.g. Hibernate, HAPI, etc.) Our HL7 parsing workflow is heavily based on Clojure with files that look almost like configuration, but actually offer tremendous power and flexibility.
Clojure simplifies and reduces the coding efforts involved in creating CloudRepo. The fact that it runs in the JVM gives us access to all the libraries that we could ever need. Our code base is much smaller and easier to reason about than it would have been had we gone with pure Java.