From Destinypedia, the Destiny wiki
Clans are groups of Destiny players, acting as a format to partake in various game activities. To join a clan, an individual must sign into Bungie.net and associate their PSN account, Steam account, or Xbox Live account to their login. Then they must navigate to the Clans home page and click "Request Join." Clans can join larger groups called Alliances.
The origins of Clans came from Suraya Hawthorne as it is a way to inspire other Guardians with the usage of Symbols and to make enemies remember them as the last thing they see before they are put down by the Guardians. With that the Guardians gains rewards for repping their clan and making them renowned for their efforts. It is a way to bring Guardians together too and accomplish other tasks in the system such as Nightfalls, Strikes, Raids, Crucibles, Gambits, etc..
Clans have a much larger role in Destiny 2. Players can form clans that include up to 100 Guardians, and create custom clan banners for their clans. Additionally, using Guided Games, clan members can assist players with a variety of activities through matchmaking, such as normal-level Raids.
After joining a clan in Destiny 2, players can acquire a Clan Banner from Hawthorne, the Clan Steward. This Banner has six levels with offset XP requirements, and clan members can only contribute a total of 100,000 XP per week. Each level grants a specific bonus:
At the end of a clan season, Clan Banner progress is reset. Clans that reach level 5 before season's end receive that season's exclusive banner staff, a cosmetic alteration to the Banner itself.
Clan XP Contribution
Every week, a clan member can contribute up to 5,000 XP to their clan's level by completing the following activities:
Reaching this milestone will also reward a Luminous Engram, so it is worthwhile to meet the contribution quota even if a clan has already hit the weekly XP cap.
Clan Engram Rewards
Clan members can acquire up to four bonus engrams if their fellow clan members complete certain activities together:
List of Appearances