Wings are a special type of equipment which function like any other, with a couple of exceptions.
You can add a maximum of two sockets to wings, and you must spend 6 Liberty Essences and some DIL for each Socketing attempt. You cannot use Socket Stones or Alchemist’s Soul to increase the chance of success, but the Stonemason’s Blessing, created via Crafting, prevents the existing socket from being lost when adding another socket fails.
Awakening a pair of wings is similar to Reinforcement, but is found under a different dialogue option when talking to the blacksmiths. You must spend 100 Liberty Essences and some DIL for each attempt. Wings can be Awakened three times, improving their stat bonuses each time. The first two Awakening stages, Eo and Xera, are guaranteed to succeed, and are added to the names of successfully-upgraded wings. The third Awakening stage, Ys, has a much lower success chance that cannot be improved, but otherwise works like the first two.
Liberty Essence is obtained by Dismantling wings via the Brand screen, and requires a Disassembly Hammer.