What is Sesshomaru's fluffy thing he carries with him all the time? (Inu Yasha)?

In the show Inuyasha, Inuyasha's half brother carries around a rather intresting fluffy/furry thing on his shoulder all the time. It's really long and as I said fluffy, but even after like, four years of watching the show, I have no idea what it is or where it came from. Please help me squash this most profound mystery by telling me what this is. Thanx! ^_^