Subclasses in Destiny 2 are a new addition, allowing you to further specialize your character beyond the class specific perks that you already get. Each class gets three further sub-classes- and these are unlocked by finding artifacts.
Why have subclasses at all? Because they unlock alternate perks, abilities, and Supers- and having options never hurt anyone.
There are three subclasses per class- and while you will always unlock at least one while playing through the campaign, you must unlock the other two by random artifact drops. No matter what artifact you get, however, classes will always be unlocked in the following order:
Titan
- Subclass Unlock 1: Sentinel
- Subclass Unlock 2: Striker
- Subclass Unlock 3: Sunbreaker
Hunter
- Subclass Unlock 1: Arcstrider
- Subclass Unlock 2: Gunslinger
- Subclass Unlock 3: Nightstalker
Warlock
- Subclass Unlock 1: Dawnblade
- Subclass Unlock 2: Voidwalker
- Subclass Unlock 3: Stormcaller