Why Is The HR department usually in charge of defining and administering performance management and appraisal systems?
Human resource departments have traditionally been "support" units where all of the day to day handling of policy and paperwork regarding personnel issues has resided. Originally, they evolved as administrative units, rather than units charged with organizational health, change implementation, and organizational leadership. While demands on HR, as a central agency in a company, have increased, much of the culture focuses on administrative functions, much like the accounting department, or what used to be called "the typing pool".
Human resources often lacks the now necessary leadership skills to plan and implement organizational change, or even to implement a properly functioning performance management system. Think of it as the legacy of being, earlier on, an administrative function.
Back to the question. Where else would you put a central function in an organization? It makes sense, at least on the surface, to "stick it" in HR. Since HR is about hiring, retention and so on, where else to put it?
The problem is that HR doesn't have the culture to support what it is asked to do. At least in most cases. They aren't trained to lead organizational change. They tend to fall back on their administrative roots, and that's why most changes to performance management systems end up "looking like the previous system, but with different colored forms".