Rabban is the Baron Harkonnen's idiotic and cruel nephew. The Baron thinks of his nephew as a "[m]uscle-minded tank-brain" (26.208). Frank Herbert must have felt the same way, because Rabban is less a character than a plot device.
The Baron puts Rabban in charge of Arrakis and orders him to squeeze the planet for all its worth. During his tenure, Rabban does just that, terrorizing the citizens of Arrakis and attempting genocide on the Fremen. Little does he know that Baron Harkonnen wants these cruel acts to make Rabban unpopular with the Arrakis populace. Then the Baron plans to replace Rabban with Feyd-Rautha while letting the tank-brain hang as scapegoat for their crimes.
Unfortunately for the Baron, the plan never comes to fruition. Rabban is killed in Paul's siege of Arrakeen and quietly disappears from the novel's pages.