Watch mode is where you take quick glances at information and notifications; app mode is where you go to “do something”. Watch mode is where most people will spend the majority — perhaps the overwhelming majority — of their time using Apple Watch. App mode is a simple one-level hierarchy for “everything else”.
John Gruber has a good analysis of the Apple Watch interaction model and the differences between the watch face and the app screen.
I've been reading a lot of comments on the Watch OS hierarchy and I've (obviously) been using my Apple Watch as much as possible for a variety of tasks and scenarios.
The more I read and try, the more I don't understand the criticism of those who claim Apple Watch should work like an iPhone. Yes, the multiple functions of the Digital Crown can be confusing initially, and I imagine that eventually there will be settings to customize what the side button does. But to argue that clicking the Digital Crown should always go back to the watch face seems shortsighted to me. There's a benefit in having an easy way to open/go back to the app screen to quickly do stuff with apps, and it will be even more obvious once a native SDK and faster apps become available.