From Bulbapedia, the community-driven Pokémon encyclopedia.
The Fashion Case (Japanese: アクセサリーいれ Accessory Container) is a key item in the Generation IV games which holds Accessories and Backdrops. There are several different sections for these Accessories: fluffs, scales, feathers, leaves/beards, head, silver, minerals/rocks, metals, elements, Contest prizes, and others. Additionally, there are fifteen Backdrops.
It can be picked up in Jubilife City after double battling with Lucas/Dawn, with two Backdrops and a few Accessories to start with. In the case of HeartGold and SoulSilver, Ethan/Lyra will give it to the player when first entering Goldenrod Tunnel.
Extra Accessories can be picked up by Pokémon in Amity Square, won in a Super Contest, found by the Massage Lady in Veilstone City, traded for Berries at the Pick a Peck of Colors Flower Shop in Floaroma Town, or given by various NPCs. In HeartGold and SoulSilver, random Accessories are picked up at random by the Pokémon leading the party while walking, won in the Accessory drawing in the Goldenrod Tunnel, or given by various NPCs. However, in HeartGold and SoulSilver they serve no purpose other than taking photos in Goldenrod Tunnel.
Additional Backdrops can be won in the Pokémon Lottery Corner, given by the lady in the Global Terminal, or won in the Accessory drawing in the Goldenrod Tunnel.
There is also a lady in Pal Park building who will give the player certain Accessories or Backdrops when certain Pokémon Game Boy Advance games are in the Nintendo DS's GBA slot.