That's related to Unity's component interface. Here's a screenshot of the Liberal Agenda game object selected in the inspector (note: your layout might not look exactly like this since I don't remember what the default arrangement is but all of the elements should be there somewhere):
https://i.imgur.com/l0vTMFL.png(linked because it's a fullscreen image)
On that object are two components, the Rect Transform (which is a default component that will be on every UI element) and the actual Liberal Agenda Impl script. The various things inside the second component are all the hooks for the public members of the class - basically this is how Unity sets the default values of a monobehaviour instead of using a constructor. So for a few examples, the UI Controller is, in the script code itself "public UIControllerImpl uiController;" - just being public exposes it to the Unity interface. Then it's set by just dragging in an object that has on it a UIControllerImpl component (in this case, the MasterController object that's farther down the hierarchy window). Not all of those references are to other objects in the scene - some of them might be image or prefab references being pulled from the asset explorer in the project tab in the bottom right. If you want to see where any of the actual referenced objects are, you can just click on them once on the LiberalAgendaImpl component and it will highlight it in the hierarchy/project window.
You might want to look up some basic Unity tutorials if you want to dig into editing the code/interface itself. Basically everything I did was very simple usage of the built in UI system, which is mostly playing with layouts, and then having some master objects to handle all the logic and read data from the game state to feed into the UI.