On the main quest battle screen, you can access your Voyages. Voyages are timed adventures where you send out your heroes to complete the task. Once time is up they will return with the goodies in tow. Voyages require certain heroes to complete, so you may want to hold onto some heroes. Oh, and do not worry about fighting for your heroes' time, as heroes can still participate in any battle even if they are sent away on a voyage.