These are some of the reasons why people fuse items:
1. Since MyShop is untradeable, some people fuse them with in-game items so they can be traded. Example, I have a Kooh Shield and someone wants to buy my shield so I would have to fuse the Kooh Shield with the in-game shield to make it tradeable. Take note that there are two items needed for fusing- one would be the base item and the other one for the image. So once I have fused Kooh Shield (image) and an in-game shield (base) I would have an in-game shield with the looks of Kooh Shield or vice versa. You can basically fuse everything except boss uniques.
2. As said above, people also fuse so that they can manipulate the looks of their character while retaining the stats of the original equips.
Hope this helps.