My Courses contains the list of all courses you are enrolled in (as student, TA, instructor, etc). This list can be edited to hide old semester courses to clean up the list so it only displays what you want to see. To do this, log into Blackboard, click My VCSU, then click the gear icon in the upper right corner of My Courses. Then edit your course list by checking/unchecking the checkboxes for each course.

To illustrate, see these screenshots:

My Courses with arrow pointing to gear.

My Courses view config page example

Remember to click the Submit button in the course edit screen when you are done editing your list.