Tartar is the buildup of plaque that can form on your teeth and cause cavities. If you become a dentist one day, part of your job will be scraping tartar off people's teeth.
Tartar is a very hard substance, too hard to be brushed off with a toothbrush. It's formed when certain elements in saliva mix with the plaque that commonly occurs on teeth. Another kind of tartar is known as "cream of tartar," and it's a common ingredient in baking, either alone or as an ingredient in baking powder. The Greek root refers to this baking tartar, tartaron, "substance encrusting the sides of wine casks."