Open tasks relevant to you appear on the Dashboard and on the Events & Tasks tab. Tap one to see its details, including which event it's linked to (for tasks tied to a specific rehearsal or concert).
From a task's detail screen you can take it (assign it to yourself) or reject it, the same actions available on the website — whichever you do, it updates immediately for everyone who can see the task, on the website and in the app alike.