Classes are guiding philosophical schools that your character follows.
Classes do two things in a functional sense: They determine your starting Stats, and they determine your beginning Skill. The unique Skill set you acquire in this manner shares the same name as the Class.
You begin with two ranks in your class skill and gain another one every five levels. A dual-Stat class begins with 2 points in two Stats, and only 1 in the remaining Stat. A single Stat class begins with 3 points in one Stat, and only 1 in those that remain.
For Common skills, available to any Class, go here.