This is in response to this blog:
http://blog.bignerdranch.com/3784-javascriptcore-and-ios-7/
Thoughts from the iOS devs on SO?
It'd be useful for running non-web-related JavaScript hosted inside your application. Think about if you had a bunch of existing code written in JavaScript that you didn't want to re-write? You can use JavaScriptCore without a UIWebView to host that code in your process. I can also imagine it being used to add user-scriptability to iOS apps. The possibilities are endless!
The other thing worth mentioning here is that UIWebView is very resource-hungry (after all, it's like running a copy of Safari in your process); It allocates a TON of memory that you will simply never get back. If you don't specifically need web rendering, JavaScriptCore can do a lot with a lot fewer resources. See my answer over here for details about UIWebView's resource consumption.