The Rod of Rassilon was one of the artefacts of Rassilon. Together with the Sash of Rassilon, it could be used to raise the control structure for the Eye of Harmony located beneath the Panopticon on Gallifrey.
The Rod slotted into the control structure (a black obelisk), allowing the person wielding it (wearing the Sash of Rassilon) to disengage the control interfaces and gain access to the power of the Eye of Harmony. (TV: The Deadly Assassin)
The Rod was also given, along with the Sash of Rassilon and the Crown of Rassilon, to Presidents upon being made Lord President of Gallifrey, believed to be of "only sentimental value". (TV: The Invasion of Time) Morbius held the Rod during his time as Lord President in his first incarnation; it was publicly taken back from him, alongside the Sash and the Coronet of Rassilon, by Junior Cardinal Borusa when Morbius was deposed. (PROSE: Warmonger)