Why does furniture often have a thin, transparent prim underneath it?

[Jennifer Boyle]

The title says it all.

[So Whimsy]

That's usually the furniture's shadow.

[Chic Aeon]

While it certainly CAN be a shadow, shadow planes can easily be added to the mesh and made as a single object (sometimes saving land impact).    BUT "shadow prims" (with or without an actual shadow) are added to  full perm mesh items so that the "creator" of the item is shown as the person that you purchased from. If the seller doesn't add a root prim to their purchased mesh object, the item appears to have been purchased from the full perm creator. It is important that it have the name of the SELLER on the item so that buyers know who is responsible for support and for questions :D. 

 

[Profaitchikenz Haiku]

Also, if the furniture itself has any complicated shapes, rotations, is sculpt, etc, it's often easier to add a pose to a "normal" prim than try and work out the sit target for the actual furniture.

[Kyrah Abattoir]

A lot of creators put a fake shadow under furnitures.

Note that it has nothing to do with the actual "shadow" graphical setting, Those shadow planes are just a static texture.