The Hand of Rathmore is the fifth artefact which Lara is looking for in the Tomb Raider III: The Lost Artifact. It was a secret fifth crystal artefact, fashioned from the same meteorite from Tomb Raider III. It's unknown if it has any relation in activating the meteorite in the Meteorite Cavern, because Lara only needed the four main crystal artefacts to activate it.
The powers of the Hand of Rathmore are unknown. However, it is implied, in-game and by the developers, that if Willard had the Hand of Rathmore, he would have become a higher being, instead of an arachnoid beast.