There are no "classes" per se. Instead, the character has a role or a background: assassin, mercenary, knight, loremaster, thief, merchant, grifter, or none. This background does
not affect your starting skills or stats. Nor does it in any way limit your character development. It merely provides a starting place.
In AoD, who you know and what they think of you is very important. The game tracks your reputation with various factions (see
this screenshot), which has in-game consequences. Factions may help you with quests if you have a good reputation with them, or actively oppose you if they don't trust you.
Your chosen background has 2 major effects. The first is to set the starting values for your various reputations (a character with the merchant background will have a good reputation with the merchants guild, for example). The second effect is to determine how your game starts.
The beginning of AoD takes the form of a vignette. Unlike in TOEE, this is not determined by your alignment, but instead by your background. The vignettes all center around the same situation (a merchant has just arrived in town carrying an interesting map), but your role in that situation is determined by your background. A character with the mercenary background will begin the game as the merchant's guard. A character with the assassin background will begin the game in the assassins guild, being ordered to assassinate the merchant (see the recent Let's Play thread). These vignettes are relatively linear and serve as an introduction to the game, the world, and at least one faction. Moreover, they all end in roughly the same place -- with you in possession of the map.
So, to summarize: your chosen background determines how the game begins and what effect your character's personal history has had on his relationship with various local factions. It does not bind you to specific skills, factions, or paths through the game. It has lasting effects, in the form of reputation bonuses/costs and the somewhat different outcomes of the vignettes, but a character with any background can take any path through the game.