In ADOM, every character belongs to a certain profession which describes what he learned in his youth. This profession is called a class and determines his special abilities and starting equipment (equipment is also dependent on race). Additionally, each class receives a skill package to account for the knowledge you gain during your apprenticeship (see the section on skills for a complete list of all skills available in the game).
Finally, each and every class will provide special powers to the character once a specific experience level is gained. The more powerful the character gets, the better these abilities will be. Some abilities are magical, some are natural talents, some are automatic, others must be used manually, but each and every ability will serve to simplify some aspect of your adventuring life.
Special powers are gained at levels 6, 12, 18, 25, 32, 40 and 50. All these special powers are usually invoked (if this is necessary) with the C-x command -- if this keybinding does not work for you check your online help (press '?'-'K').