The Soul Reaver is a sword that you get off of the second boss (Kain) after you beat him, he smashes it over Raziel's (The guy you play as) head.

This act releases it from its physical prison and it bonds with Raziel & sustains his strength in the physical world (Without it you gradually loose strength in the real realm) The Reaver appears as a wavey sword with a constantly swirling aura around it and Raziel's arm and can only manifest it in the real realm and at full energy.
It is always with you in the dead realm.

The Reaver can also be transformed into the Fire reaver, Kain reaver (Without inputting a cheat I don't know how to get it) and the Ariel Reaver (Again the cheat is the only way I know how to get this)