Why does Apple Mail copy messages to an "Important" folder?

Apple Mail (version 16.0, running on Monterey 12.3.1) has set up mailboxes "Important" and/or "Archive" on various of my mail accounts, and copies incoming mail from the relevant Inbox to one or other of these. I then have to go in and delete stuff I have already deleted (from the Inbox), and it's unclear whether deleting a message in one of these places will also delete the corresponding message in the Inbox. I never asked for this behavior, or for these extra mailboxes, and I want to know how to get rid of them and the behavior that puts stuff in them. I find that Mail won't let me just "delete" these mailboxes. What is going on? I just want to see (a single copy of) my incoming mail in an Inbox, and either delete it, move it to a specialized folder, or just leave it.