Using Item Synthesis, you can take the appearance of one item and fuse it with the stats of another. This is purely for cosmetic reasons, and as such makes it extremely important if you want to be strong AND fabulous.
How to Unlock:
First, go to Fareast city, and enter this building near the center of the map.
Talk to either of the shady folks inside. When a text box comes up, answer, "Friend of Enigma Group"

You will get an Enigma Group Pass if you enter it correctly. (You have to repeat this every time you want to enter the Fortress.)
Now head to the field north of Fareast City, and talk to the NPCs at the top of the map to let you into the Enigma Group Fortress. (They will take your pass.)
Go into the building directly in front of you and talk to Leader Buru.

Walk through the door behind him, and select, "Go to Holy Mother's Island."
Head into the painfully obvious house and talk to Yoko to deliver the medicine Buru gave you.

Go back to Buru with the mask Yoko gave you. He will give you more medicine to give to Yoko, and doing so will finish the quest.
How to Use:
Make sure you have both pieces of equipment you want to fuse in your inventory (un-equipped). Talk to Yoko to open the synthesis window.
First select the item whose image you want to use under the "Appearance" column.
Then select the item whose stats you want to use under the "Ability" column.
The process costs 20,000G and has an 80% success rate. (If it fails for you please post what happens.) Now just pay up and hopefully enjoy your fused item! o/
Limitations:
-When fusing weapons, they both must be the same equipment type.
-You cannot fuse armor that have completely unrelated equipment slots.
-When fusing armor, they don't have to be the exact same equipment type in order to fuse them. It seems as though the appearance item must take the same equipment slots (or less) than the ability item. (e.g. the Tiger Mask and Corsage above)
-The race, faction, and gender requirements of the two items must match.
-Both items must be usable by the same job class.
-The appearance item must not be a higher level than the ability item.
---In Progress---
Please correct me or tell me additional rules you discover.