Sturdy Elytras adds the Sturdyness Enchantment to the game. In the Late-Game Elytras tend to be far too fragile, especially for technical Players flying thousands of blocks. Constantly having to swap to a new one from your Enderchest is just annoying. The Sturdyness Enchantment can only be applied to Elytras and acts similarly to Unbreaking. It can be used alongside Unbreaking as well.
To use this mod properly, it is required on both client and server. If only installed on the client, but not the server, it's just not accessible, but you can play no problem. If installed on the server, but not the client, you won't be able to see the enchantment, but it will still work no problem, if someone with the mod makes an elytra for you.