I want to be able to change some of the user's settings and profile information when they are banned and/or unbanned. How would I go about doing this? I'm new to MyBB plugins. Thanks for your help.
http://docs.mybb.com/ -> Plugin Development
As for the specific action, you need to hook to
task_usercleanup (detect expiring bans, may be tricky looking at the task code..),
modcp_do_banuser_start,
modcp_liftban_start,
admin_user_banning_lift_commit and
admin_user_banning_start, then do what you want there.