Dark Magic is any spell that is meant to maim, hurt, or kill. There are three levels of Dark Magic,

Jinx: jinxes are meant mostly for jokes, the least painful and lowest of Dark Magics. 

Hex: slightly more painful, mostly used by students at Hogwarts when dueling. Hexes are meant to cause discomfort, such as the Bat-Bogey hex, which turns ones snot in to bats that fly out of the nose.

Curse: curses can range anywhere from the Curse of Bogeys to the Killing Curse. Curses are the darkest level of magic. The three Unforgivable Curses(to be talked about more later) are some of the few illegal spells.

Dark magic is not illegal, and some spells will be taught in this book.

Advances in Dark Magic are almost always huge, from Herpo the Foul's discovery of Basilisks to Voldemort's seven Horcruxes.