In the accessory shop, you can buy apparel to equip on your characters. Each character can have one hat, face, arm, and body accessory. These accessories will show in battle and in scenes except for the body accessories (Bath Towel). You can move the accessories around between your characters freely. Sometimes, you can give accessories to your characters on the MyCastle map, giving support points between that character and your Avatar if you give them something they like (which, from experience, will usually not be a Bath Towel).
While accessories are mostly for jazzing up your characters, they do have additional effects. Most will boost or reduce damage in MyCastle battles; however, some will increase the chances of the wearer manning a specific shop!