So when I moved to a new Mac, I ran into the problem that Apple Mail does nicely retrieve my emails, but no longer showed the sub-folders of an account underneath the "smart mailboxes" on the left side. Quite a bummer, since I was so used to working with the subfolders in that way.
It took me a while to figure out how to resolve this and/or what was causing this - typically this seems to affect IMAP accounts.
To fix this, in Apple Mail, go to the menu "Mail" - "Accounts" and click the account affected by this problem.
There you'll find an "Advanced" button, click it.
In the upcoming window, you'll find a box called "Path Prefix", which most likely is empty.
For most mail servers, you should enter here "INBOX" (without the quotes of course) and click "OK".
I had to restart Apple mail after that to see the effect.
Note:
You might have to do a "Mailbox" - "Synchronize all accounts" or a "Mailbox" - "Rebuild" before restarting Apple Mail.
Unfortunately I had tested both before restarting Apple Mail so I do not know if this had an effect or not.