Thank you all. I think, I got it.
The modal, to try and sum it up, is a way to step out of the normal flow of the app so the user can accomplish something prior to continuing on their way.
And the example for understanding:
For example, go to the Settings app -> Mail -> Add new account (all presented via a navigation hierarchy) - choose one of the providers and a “login page” is presented, modally. Once you fill it out and the whole thing is confirmed, the modal disappears and you are back to your account list. Another example is in the Calendar app, when you add an event, which takes you out of the process of viewing events, the view is presented modally - when you go to assign a calendar, however, the view is presented hierarchically.
PS there quotes of Josh Bruce