However with Nashhorn it seems that now we can reuse the same validation as written in Javascript.
Hm... I don't think I'd want to resort to JavaScript for that, with all the language and context switching that entails. Most web frameworks have validation anyway built in.
Another would be for example stated as given earlier that there are many javascript frameworks doing much stuff on the front end. If you wish to reuse that in Java that would be problamatic. But with Nashhorn this is now possible.
I don't think too much of that code would be reusable, given how it's meant to run inside a browser, but I could be wrong about that. In that respect, Nashorn doesn't add anything new, though - the quite capable Rhino JavaScript implementation has been around for 15+ years, the last 10 even included in the JRE via the javax.script API.
I think major applications will be scriptability and customizability of applications (both client and server). Client is not very relevant these days, but having the ability to implement certain parts of server side code as JavaScript facilitates easy changeability at runtime. That could either be core parts of the business logic, or extension points for future changes.