A character's Class defines the basic Skills of a character - what armor the character can wear, what weapons and tools it can use, what Logos Abilities it has access to, etc.
Unlike most other, traditional TTRPGs, Tabula Rasa does not force the player to pick a class when a new character is being created, which the character will keep for the rest of his "life". Instead, all characters in Tabula Rasa start as the same Class ("Recruit") and evolve through a tree of Classes. At every Tier, a major waypoint in the character's career, the player may chose between two more specialized career options: http://vnmedia.ign.com/tabularasavault.ign.com/images/subfeature/classtreelrg.PNG
The shield on top is the Recruit. The two swords to the lower-left of Recruit is Soldier. The two flags to the lower-right of Recruit is Specialist. Every Class is able to utilize the Abilities and Trainings of all its root Classes, e.g. a Grenadier may also use the equipment of a Commando, Soldier and Recruit.