Basically, any character type you're used to playing in the Dragon Age series is an unlockable class. You'll start off the progression system with a sword and board dwarf class, elf caster, and human archer unlocked (with nine total classes available at launch). Each of these classes has their own skill trees to unlock via experience points, special weapons to find, and armor to collect and customize. As you progress, you can unlock more specialized classes with unique skills, such as the two-handed weapon-wielding Reaver, fireball-throwing Elementalist, and stealthy Assassin.
Like Mass Effect 3's classes, Inquisition's level individually and share a loot pool. So, if you find an awesome shield playing as an Archer, you can equip it to your shield-bearing Legionnaire later on. It's always a good idea to keep more than one class equipped and ready for battle because joining a group in which all players are the same exact class is a surefire way to wipe. Variety wins the day in Inquisition's multiplayer.