I'm trying to figure out how the information is stored on the app. You can update the app on the website, and then the app running on the simulator is updated. Does that mean that the final app (installed on an iPhone) is updated from the web as well? As in, it won't work offline, or on the iPod touch? Thanks in advance.

There are numerous ways to explain this, and the answer depends on many factors. Generally speaking, the app downloads it's configuration data from the web and stores it locally so it can operate offline. However, there are many screen types that you may create that do require an internet connection to work. Example: If you create a CustomURL screen, it would need an internet connection to load. But, if you use other screen types, it will not. So...it all depends on what your making ;-)

I am mostly using the custom text. That's what I was mainly asking about. Thanks.

The CustomText screens download the data from the web and cache it locally. This means you should not need an internet connection to load the screen after it's already been loaded the first time.