A class skill is a skill which a class has affinity with (e.g. the rogue class has a focus on stealth so it has both hide and move silently as class skills). Those skills which a class is not so able with are considered cross-class skills (e.g. a rogue attempting a direct fight).
With regards to creatures in general, a class skill is any skill in which a monster has acquired at least one rank or in which the creature has a racial bonus.
Improving class skills[]
A character may buy class skills at a rate of 1 rank per skill point.
The maximum rank for a class skill is 3 + character level.