SO, MaxPass is basically just like the old paper FP system where you would go to a kiosk and scan your ticket to receive a ticket with a return time, except you can use your phone to pull them instead. As soon as you are scanned into the park that day you can start making FastPasses through the app at either park. Once you confirm a selection, you can get another one after a certain amount of time has passed (I do not know the exact amount of time - I think a hour) or once you use the one you made. If you do it right you can use a lot of FastPasses! You can hold several FastPasses at once, but you can't have more than one for the same attraction at the same time.Some of the most popular stuff will start to show late return times or run out completely eventually depending on how busy it is.
One note about FP at DLR is that not all rides have it at all. When WDW went to FP+ they added it to almost every single attraction. At DLR the selection is limited, mostly for the "bigger" rides. Things like Peter Pan and the other Fantasyland type stuff do not offer FP at all. Also, for shows you will still have to go to the proper kiosk and pull a paper ticket (Fantasmic!, World of Color, Frozen Live at the Hyperion). These FPs are not connected to your ride FPs and don't hinder your next selection time.
Hope that helps.