If you're interested in understanding more about the internal operation of TiddlyWiki, TiddlyWiki Architecture gives an overview of how TiddlyWiki is structured. Then read the code – start with the boot kernel $:/boot/boot.js.
The key to understanding how it works internally is to see that the RefreshMechanism requires that any region of the DOM can be regenerated at any time. This means that the entire state of the user interface must reside in the tiddler store, from where it is synchronised into the DOM. This is done to improve performance by minimising the DOM interactions during the refresh cycles.
It also determines the standard UI flow:
From a technical perspective, TiddlyWiki is a fairly classic MVC architecture, with strict separation of concerns. The model is the tiddler store, the view is a rendering tree (such as the one created from $:/core/ui/PageTemplate in startup.js), and the controller is the core code itself.