IMAP is basically a file access protocol (think FTP), but the "files" are emails. You don't have to just pull from an INBOX and save emails in Sent (that's done over IMAP, not SMTP), you can read/create/modify anything anywhere, so some apps save notes to IMAP for some reason (to replace "self-emails" I guess).

IMAP is read/write and holds the mail on the server (unlike POP).

If you go into your internet accounts settings and tick "notes". Notes will surface it and stores notes in folders on the mail server. (Not all of notes functionality is available in the notes stored in those folders.)

That's a big proviso in parenthesis. I would go as far as saying that most functionality is not available, unfortunately.

Apple’s visual voicemail on the iPhone also syncs using IMAP hosted by your carrier.

So does the Notes app, at least for Google accounts.