Here is a fairly balanced discussion of tail docking in Yorkshire Terriers:
Yorkie Tails | Docking | Guidelines | Methods | Pros and Cons. Nowadays, it is done purely for appearance and to conform to breed standards for purposes of dog shows. Our Bella's tail was docked, but I wish it wasn't. I've watched videos of tail docking, and although they say that the young puppies don't feel the pain as much, it looks like a horrible procedure.