In general I find as strong points for clojure (in no particular order):
1) The REPL to try things out interactively.
2) Everything is immutable by default and mutability has several well chosen standard patterns to modify state in a safe way in an multithreaded environment
3) Tail recursion is made explicit. Till there is proper support for tail recursion on the JVM this is probably the best compromise
4) Very expressive language which favors a functional approach over an imperative approach.
5) Very good integration with the Java platform making it painless to mix in Java libraries
6) Leiningen as a build and dependency management tool together with the clojars site
Ok, point 6 has nothing to do with the language perse, but definitely with my enjoyment of using it.
Regarding applications it targets multithreading applications, but the way things go right now that could mean about anything, as everywhere people try to keep all those cores busy while the user is not waiting. On the other hand apparently a lot of people use it to deploy to Google App Engine which is radically SINGLE threaded.
The functional approach works well in my (limited) experience for implementing data transformations and calculations. Where information and events can be 'streamed' through the application. Web apps fall largely under this category where we "transform" a request into a "response".
But I still have to use it in real production code. Currently I use it for personal projects and prototyping/benchmarking stuff.