Furniture Packages are the packages you get when buying certain types of furniture. They come in different sizes, depending on the item inside.
So when, for example, you buy a Big Table at one of many Furniture Shopkeeper NPCs, instead of the big table you just bought, you will get a furniture package that contains the big table. This was done because furniture cannot be picked up and people who bought furniture had to push it all the way to their house, possibly having it stolen on the way there.
Since update 10.92 you can no longer "use" a furniture kit to open it, and it will not cause a spark effect anymore if you try to. In order to open it, you now need to right-click the furniture package and choose "unwrap". An item can be rewrapped by right-clicking it and choosing "wrap".
All big furniture packages look the same as a Heavy Package and all small ones look the same as a Mysterious Package.