Glossary · Mailboxes
IMAP import copies existing mail from an old mail server to a new one over IMAP, keeping folders, dates and read status.
The new provider signs in to the old account over IMAP, usually with an app password if the account has two-factor authentication, and copies each folder across server to server. Nothing has to pass through your computer.
Run it before switching MX records, then once more afterwards to pick up mail that arrived in between.
Every domain you run in one inbox, from $3 a mailbox. 14 days free, no card.