Class is a characteristic of a Unit that futher defines its abilites beyond those of its Race and Level.
In the context of non-Casters, class appears to be a categorization of the unit's role and in combat. A unit may be promoted to a higher class, such as hobgobwin units whom Stanley promoted to Knight-class.
In the context of Casters, class appears to be a designation of power level. Wanda Firebaugh is a Master-class Croakamancer; Janis is a Master-class Hippiemancer; Maggie has more limited powers because she is only an Adept-class Thinkamancer.
It is unclear whether a Caster can achieve a higher class through leveling, through training, or through Schmucker-expending promotion.