This is really too broad a topic, but I'll give a mile high view and show you some videos that dive into more detail.
In the current iteration, the high level view works the exact same way as in "How Does Appcelerator Titanium Mobile Work?", the main difference is that now Android uses V8, iOS uses JavaScriptCore, and they have added an MVC layer on top of Titanium called Alloy that lets you split things up nicely.
The two main platforms do things fairly radically differently under the covers, check out this video on iOS internals, and this one on Android internals.
The view system works by native objects being wrapped by JavaScript objects, with a bridge between them that sends eventing information and updates. If you really want to know more, just look at the source, but that is not at all necessary for development.
But, all that is about to change with Ti.Next, which will be a fundamental shift from cross-coding UI components per platform, the core engine will be the same across platforms, and written in ASM generated code, all that to say, don't get hung up in the details, just code the thing.