From Destinypedia, the Destiny wiki
Upon starting the game, each Guardian class begins with one Common Emblem in their inventory.
These Emblems can be acquired by players through normal gameplay, including single-player combat, Crucible matches, vendor purchases, and Age of Triumph milestones.
Raid and Arena Emblems
These Emblems are earned from completing Raids and Arena challenges.
Code Redemption Emblems
These Emblems can be acquired by any player who redeems the following codes on Bungie.net. The codes do not expire and can be redeemed by any player. In the game, the Emblems can be retrieved from Tess Everis at the Tower.
These Emblems are available only to players who meet certain requirements or complete limited-availability quests and events.
The below emblems required a purchase outside of the game or paying a premium price in order to obtain.
Emblems that have been altered or converted into other Emblems listed above; the name, rarity, and/or image of the Emblem may have been changed during development for unknown reasons.
The Emblems are present in Destiny game files, but the requirements for unlocking them are unknown. Some are possibly Emblems that are reserved for Bungie employees and/or select distribution during future special events.