Why?
Archiving is useful for when you're done with a course, but would still like to keep all the assignments, notes, attachments, and so on. Think of archiving as a way to hide a course, so it looks like it doesn't exist!
How to Archive
Go to any of your courses, and click the "Edit" link.

To archive it, just check the box next to "Archive" and click "Save Changes." The course will no longer be shown on the Courses page.
Showing Archived Courses
To show your archived courses, click "Show archived courses" near the bottom left of the Courses page. (This link is only visible if you have any archived courses.)

All the archived courses will be visible, and have a lock next to the number of assignments it has.

Courses can be archived and un-archived (just uncheck the box next to "Archive") any time.