Sulfuric acid dehydrates sugar. That sounds pretty tame, until you see that "dehydration" means that a huge, black, sugary pillar crawls up out of the beaker and comes after you.
How much damage can sulfuric acid really do? That depends primarily on what it comes in contact with. While it can do a lot of damage to metal (and of course to human skin) one big no-no for anyone working with sulfuric acid is putting it in contact with water. (Yes, water is used to dilute acids, but the practice is to always add a little acid to a lot of water, and not water to the acid.) The sulfuric acid will jam an extra proton on the water, making the water into H3O, and giving it a positive charge while the acid has a negative charge. This process gives off a lot of heat, which can cause the entire liquid to boil violently. People who add a little water to acid will often get splattered with concentrated acid as the liquid boils. No problem, right? How hard is it to keep water away from acid?
More things have water in them than you think. Cotton has water, or at least hydrogen and oxygen, as part of its structure. Sulfuric acid will rip that off, destroying the cotton in the process. Sugar also has water molecules in it. A sugar molecule is about twelve carbon atoms with twelve water molecules attached to them. That's a lot of water for the acid to liberate from its carbon bonds, and it goes about the process with gusto.
First the mixture will collapse down as the acid wets the sugar. It will also turn slightly yellowy. So far it's no different from water mixing with sugar. Then things get weird. The mixture turns black and gooey. The color is the result of pure carbon atoms getting loose. On their own, they're black. Then the mixture starts to heat. The heating water and the expanding stack of carbon atoms push up a porous column of graphite, while the water boils and escapes as steam from all the nooks and crannies along its surface. Depending on how much acid and sugar were in the container, this can go on for a while, pushing up snakes of carbon that eventually break off and allow the mixture to push up more. There's also the faint smell of hot sugar, which some people compare to roasting marshmallows.
Not all the acid is used up in the reaction, however, and it will boil along with the water and escape as steam. This means that whoever is nearby will very likely be breathing in sulfuric acid, which is (at the best of times) not an ideal situation. That plants this experiment firmly in the "don't do this at home" category.