Classes define the rules by which kids are generated, determining their possible stats, starting items, equipment, and traits. For instance, Bully kids generate with a breastplate, cuirass, or chainmail armor, while Poets start with a jacket or robe.
In addition, each class has a special ability unique to them which can be activated by pressing the Class Skill button (or by moving the right joystick on gamepads). These abilities can often be improved by advancing your kid's class at the Ghost that appears every 3 floors; every class can be advanced twice this way.
Each class is based on one of the six stats, with the class' associated base stat starting at 5 (except for Bully), while all other stats are lower. Alongside their "strong" stat, each class also has two "weak" stats, that start lower than their other stats, and lower than those same stats of other classes. These "weak" stats alternate being in the bottom slot on the level-up menu, making them slower to improve relative to the other 4 stats.