You must give an assignment a grade in order to finalize the grading process. Until a grade has been selected, Handouts will allow you to continue working on an assignment and the option to submit graded work will not appear.
Once you have selected a grade and saved the changes, a yellow tab will appear above the assignments giving you the option to 'SUBMIT ALL GRADED'. This allows you to choose between submitting graded assignments as you go, in segments or once you have finished grading assignments for the whole class. Simply tap on 'SUBMIT ALL GRADED' when you are ready and the graded assignments will instantly find their way back to the students!
You can also finalize grading using the Quick Grade function. Quick Grading gives you the option to return assignments to students without giving a final grade. This is useful for acknowledging that a student has completed an assignment where an evaluative grade is not appropriate, e.g. where the assignment is to read a piece you sent them.