What is the Archive folder in Mail and why is it synced to Gmail?

That would depend on how you have the settings at the gmail website. Gmail's default is to archive deleted messages. Also, the All Mail Folder from gmail is normally mapped to the Archive mailbox in Mail.

I suggest going to the gmail webmail site and open Manage Labels. Hide the All Mail Folder by unchecking the box to Show In IMAP. That will remove it from showing in Mail's archive.

Also, go the Forwarding & Pop/Imap tab and check the settings on how gmail handles deleted messages. You can make changes there if needed.

Unless you want to archive every email, then yes you can change it to delete. If you want to save specific emails, then you can move them to other folders you create.

Everything I do is controlled in Mail and I save only messages I want. My settings are:

Hi Joe-ATV:

Have you checked your mail preferences?

Here is what mine looks like.

Kim

It seems normal if your gmail account is set up using IMAP (which is the default).

Your emails are Googles revenue, instead of deleting them, they archive them for future sale. The folder is not from Apple mail, it is from Google.

If you want the emails to be deleted when you delete them, yes.