Hello sbgorski,
A clan is a group of people with a same interest. A clan play together Destiny, train together, make raids, crucible, etc.. is like having a big group of friends. A clan is really needed in Destiny, especially if you want to do some raids and the Vault of Glass. You will need a team to do these two. You can go to the clan section and look for clans.
Cheers!
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Thx :)