How do I purge deleted e-mail messages from Outlook?

What does "purge deleted messages" mean?

When you delete an email from your IMAP account, depending on your email client configuration, it may go into a Trash folder, or it may be depicted with a strikethrough (like this).

If you choose to purge deleted messages, emails with a strikethrough which you had selected to delete will be permanently removed from the server. It's like clicking "Empty Trash." There is no way to recover a purged message.

Won't copies be saved on my other computer?

No, unless you configured your email client to do this for you. If you permanently delete an email message from your IMAP email account using webmail or any email client, that message is gone.