How do the mail folders on my Mac and folders in Gmail relate?

I have to make an assumption her that your email app is set up to operate in an IMAP mode. If so, then whatever yo do in your email app is mirrored on the email service provider's web site. You can visit the web site directly by using a browser to do so. Put another way, you will normally have the same folders on the web site as you do in your computer and they will both.contain the same messages.

If your email service has been set up to function in the POP mode, whenever your email app requests a download of any available messages which have been received on the server, they will be downloaded to your computer and are then deleted from the server automatically. I hope this answers your question.