Archive mailboxes?

I'm running Sierra on an iMac (fairly recent vintage). When I switched to Time-Warner cable, I noticed that I had, in addition to my usual mailboxes, two sets of Time-Warner mailboxes for each of two accounts. These contain the following mailboxes: Deleted Messages, Junk, Junkmail, Sent Messages, SentMail, and Trash. I also have an "Archive" mailbox, which I didn't create, which itself contains three mailboxes called "On My Mac". There's a message in each one - the same message. I don't recall putting it there.

Why are these mailboxes there and can I delete them. The T-W mailboxes I can sort of understand as being default mailboxes that were created when I switched to cable from DSL. Not sure why I need the Archive mailboxes though.

I've enclosed a JPG.