They have the power of Judge, Jury, and Executioner over individuals or whole worlds. They can command civil authorities, the Imperial Guard, the Navy, agents of the Officio Assassinorum, even the Astartes (though they are wise enough to tread carefully in the last case, usually requesting their help instead of just ordering them around). State Sec with a side of Church Militant, Inquisitors are some of the most powerful individuals in the Imperium, working behind the scenes to keep everything from going (further) to Hell.
In Warhammer 40,000, the Holy Orders of the Emperor's Inquisition (referred to as simply the Inquisition) are the men and women whose task is to police all aspects of Imperial culture, rooting out threats that are not necessarily military in nature but which threaten the very structure of the Imperium.