Including that link in your original question would have been helpful.
When I went to
http://office.microsoft.com , clicked on the Templates
tab, and searched for "fourth coffee business card", I only saw
http://office.microsoft.com/en-us/templates/TC101316731033.aspx which is
an Outlook 2007 template.
The background in your template is a picture formatted as "behind text".
There isn't much you can do to a picture in Word because Word is not a
graphics editor. So when you say "can't figure out how to change the
background", I'm guessing you can't figure out how to put a different
picture in there? To do that, first you need to add the "Select Drawing
Objects" tool from the "Commands Not In The Ribbon" group to your Quick
Access Toolbar. Then click once on the Select Drawing Objects tool to
activate it, use the cursor to draw a big box around the eight
background pictures in the business card template to select the
pictures, press the Delete key to delete the selected pictures, and
click on the Select Drawing Objects tool to turn it off. Then insert
the picture you want, format it as "behind text", and Ctrl+drag to
replicate.