The Dressing Room is where you can customize your character's outfit. You can earn new articles of clothing by purchasing them from the store, completing certain missions, or as DLC.
You can also create and save favorite outfit sets so you can change on the fly.
You also have the option of creating a Diorama of up to 5 characters posed in a specific scene.
Note that the character badge accessories are unlocked by completing a certain amount of waves in Survival Mode on the different maps (each map has a specific 5 badges, one available for every 10 waves).