The Inspector General is an investigator charged with examining the actions of a government agency or organization, such as Starfleet or the Federation. Their job is to look for the possibility of misconduct, fraud, or criminal activity by individuals. The Starfleet Inspector General is also part of Internal Affairs.
In 2364, Dexter Remmick and Admiral Gregory Quinn were sent by the Inspector general's office to look into possible misconduct aboard the Enterprise-D, Captain Picard specifically. (TNG: "Coming of Age")