Class perk set is the sum total of perks chosen by player.
Typically each group of perks(represented as a drop-down menu), allows selecting one perk per group. Each perk is a unique bonus applied to character permanently.
Players may pick a class based on perks provided, instead of other way around, so some system allow class-less combinations of perks(harder to balance).
Ideas for perk groups are usually themed with central motif(e.g. ancestry) or feature(trait) specific to class/specialization and give bonuses related to specialization.
These perks usually don't appear on items(perhaps excluding top-end gear) and significantly influence gameplay - balancing their effect is central to fair class balance(that is the reason most games omit class perks to avoid balance issues).

High-level perks usually appear as character reaches specific level(e.g. 40,50,100) and allow choosing another perk from a new group specific to that class.
Sub-classes/specialties can be replaced by this system alone to add flexibility.