Besides the social, there are a couple of other benefits, but nothing terribly game breaking. Speaking of the social aspect, it is barely there. There is a chat channel that barely gets used in the clans I have been in and that’s about it. You can’t even see basic things about clan members like whether they are online or not or how long it’s been since they have logged in.
As for the other benefits…
In events, your clan is ranked on the leaderboard and all clan members get rewards depending on where your clan ranks. If your clan ends up ranked #1 all members get 150 gems and 2 shiny tokens.
As your contribution to the clan increases (you can see this on the “members” page in your clan UI), your Trophy Points will go up. Once you reach certain levels, you get an XP bonus for your birds. For example, my current Trophy Bonus is 1360 and I am at the 1300 level which grants me +10% XP.
You have the opportunity to buy items that benefit all clan members for 24 hours. My clan is only level 2, so the only item available is the First Aid Kit Rank 1, but if one of the clan members purchases it, all members get the benefit of it.
It is possible there are other benefits I don’t know about, but those are the ones I do.
I run the Weeping Angels clan. I think the biggest thing clan members want is just people to stay relatively active. There is no sense in having players taking up slots that quit playing the game. That’s one reason level requirements to join are popular. A newbie starts the game, plays for 3 days, and loses interest. No sense having them sitting dormant taking up a clan spot, since spots are so limited.