Sugar is a type of carbohydrate. It turns out there is a whole class of carbohydrates called "sugars." The kind of sugar we usually think about - table sugar - is called sucrose. Sugar is made up of carbon, hydrogen and oxygen atoms. It's the way these atoms are connected that makes each type of carbohydrate different. In each molecule of table sugar there are: 12 carbon atoms, 22 hydrogen atoms, and 11 oxygen atoms.
The black stuff is called burnt sugar! But seriously, this is what happens when you heat or burn things that contain carbon. It reacts with oxygen and "oxidizes" (burns). The black stuff itself is mainly carbon. So is the soot inside a chimney.
Unfortunately, the bacteria in your mouth also love to eat sucrose (more than you do). When they do, they produce that yucky stuff called plaque that rots your teeth and gums.