Clan rewards are special accessories in the shop. These are locked, and may be unlocked by playing in a clan.
Every two weeks on Friday the Clan leaderboards reset, and rewards are unlocked for all Clan members. All members of a Clan will unlock the same item. You have to play at least one game in Quick Play or 2vs2 with your current Clan to receive a reward. What item is given depends on the Can's position in the list as well as the rating earned.
The Clan reward is affected by how many clan members already own the reward, so it's possible for a clan to unlock the same reward twice if there are a lot of new members who don't own it yet.
Clan rewards are unlocked by playing in a Clan, but you have to buy the items using coins or gems if you want to use them.