The File Manager is a tool showing you all of the files you have access to for any of your current courses. It shows you files for all courses and for all assignments in each of those courses.
To add a file, find the 'Add file' button for the course or assignment you wish to add it to. You'll then be presented with a form to upload your files. Click 'Save' to save the file to that course or item.
Of course you can! 'Drag' means you can drag the course and all of its files to a different location in the list. You have complete control to reorder the course list in this page. It will automatically save your preferences for when you come back.