For flash (non-mobile) assignments, you can adjust due dates and available dates for individual students or groups of students. When adjusting the due date, we call it an extension. When adjusting the available date, we call it an offset. Extensions/offsets for mobile assignments are not yet possible.
If you need to give a student or a group of students more time to finish an assignment, you can grant them a per-assignment due date extension. If the same set of students will always need more time (for example, a class period that meets the next day) then you can set a course-wide group extension. For more information, see the help articles Due Date Extensions and Available From Offsets and Group Offsets and Extensions.