The Tall Man's Finger is a Legendary ring in Diablo III. It requires character level 31 to drop.
Life of the big dog is roughly +350% higher, and damage roughly +60% higher (for both melee blows and skill rune effects), than that of the lesser dogs combined. However, it is less effective at blocking enemies' pathing than several dogs. For the purpose of Sacrifice, the damage from explosion is tripled (to 3270%) regardless of how many dogs have been merged.
After patch 2.0., it was bugged and allowed any pets of any class to be buffed accordingly. This was dealt with in a hotfix later, making this ring's affix only work with Zombie Dogs.
This finger was severed from the hand of an Umbaru priest who crossed over to Mbwiru Eikura in search of knowledge and came back...changed. Before the unclean phantasm was finally slain, he evinced great power over the dead, and this metal-plated digit still possesses some of that power.
This ring is a possible reference to the Tall Man, a character from the Phantasm movie series (hence the description).
As of patch 2.2.0, as a pun on this ring, another one called Short Man's Finger was introduced, granting the exact opposite effect on Gargantuan spell as The Tall Man's Finger has on Zombie Dogs.