From Destinypedia, the Destiny wiki
Upon starting the game, each Guardian class begins with one Common Emblem in their inventory. Subclass specific emblems are earned as they are unlocked.
These emblems can be acquired by participating in limited-time seasonal events, by completing certain challenges and quests during a season, or by ranking up Season Passes.
These emblems can be acquired by players through normal gameplay.
These emblems are obtainable from reaching certain scores in the Nightfall.
These Emblems are earned from completing Raids and Raid Lairs.
Scourge of the past
These Emblems are available only to players who meet certain requirements or complete limited-availability quests and events.
Unknown Emblems (not released yet)
These emblems have either not had their unlock conditions discovered or they have not been released yet.
The following emblems have been modified in the game.