Furniture is a class of items that can be placed on blocks, or hung from them, usually to become background objects that characters can move over and through. Some are functional, such as crafting stations, Chests, Beds and light sources (among others), while many are mainly decorative. Most furniture items are sorted into sets. Most placed furniture can be freed with a pickaxe.
Items that must be hung from "ceiling" blocks (the underside of blocks) cannot be hung from platforms, unless said platform is hammered into its lowered position.
The Emphatic, Untamed Calamity Mod adds a couple new pieces of furniture, with no new furniture sets as of yet.