The Exorcists are the overarching antagonists of the entire Hazbin Hotel / Helluva Boss universe, though they have not appeared in person yet, instead they are revealed in a flashback but are pivotal - since the entire plot of the Hazbin series revolves around their imminent return.
The Exorcists are a group of militant angels dressed in elaborate masks who are tasked with traveling into Hell every year and going on a bloody massacre, killing as many demons and sinners as they can before returning to Heaven and waiting for the next year to arrive so they can repeat the cycle over and over.
This is done to stop overpopulation in Hell as it is only via angelic weapons that demons and sinners can permanently die, the Exorcists greatly enjoy their role and are stated to be extremely sadistic creatures who take great pride in killing others.
While many accept the vicious cycle of death each year things change when Hell's resident princess, Charlie (daughter of none other than Lucifer himself), seeks an alternative to the annual purge in the form of the "Happy Hotel", a place she believes can redeem sinners and allow them to enter Heaven, thus solving Hell's overpopulation issues without resorting to erasing others.
While the Exorcists have not shown in person they are by far the greatest danger to the entire setting, their regular purges also cause angelic weaponry to be left behind - these weapons are used by demons and overlords to erase their competition and thus even without direct conflict the Exorcists play a massive role in bringing lasting danger to Hell (it is unknown if they leave these weapons on purpose or by accident, though since they have been stated to be sadistic creatures who enjoy death they likely deliberately leave these weapons for residents of Hell to find and thus cause more destruction).
One of the creator's writers (Dave Capdevielle) went into details during a live-cast on what happens when demons die in Hell, he stated they become completely trapped forever in a void of nothing and even their former friends and loved ones forget they exist - thus they literally become erased from even the afterlife.. this would make the fate of those that fall victim to the Exorcists' annual purges truly nightmarish even by the standards of the already dark setting.