As is implied by the answers, Word 2013 shows Compatibility Mode in the title bar if a document is opened created by an earlier version, or if a document is created using a template created by an earlier version. It is easy to fix for new documents without jumping through hoops.

Open the normal template: File > Open then browse to the template.

If you have not changed the default location enter or copy
%appdata%\Microsoft\Templates
to the address window of Windows Explorer and you will be taken to the folder that contains the default template - which for Word 2013 is normal.dotm. Note that this folder is normally hidden.

Then SaveAs in the same location with the same name. This will update the template to Word 2013 standard.

Repeat for any older document templates and add-in templates that you have created yourself (though to be fair the add-ins will not cause this issue).

__________________
Graham Mayor - MS MVP (Word) (2002-2019)
Visit my web site for more programming tips and ready made processes www.gmayor.com