New mail count on Dock icon?

Normally, the Count would be directly related to New and Un-Opened e- mail in one of your inboxes ( if the user has more than one e-mail account configured to Mail )

At least, that is how it works on all three Apple Computers I am running.

Give us a Screen Shot ( without any personal info revealed ) of the Inbox(s) and Archive boxes and post back if you would please.

Within Preferences for Mail.app, on the General tab, there's an option called "Dock unread count" with the options "Inbox Only" and "All Mailboxes". Which option is selected in yours?

Sorry and you are right. 😔

Was taken with Lord Of the Rings is initial screen shot.

To answer your later question

EDIT - I had missed that P. Phillips already covered this.

In Mail->Preferences, what do you have selected for "Dock unread count"?