Priests are invokers of Light and Darkness, divine forces with a divine order that the disorder of the Burning Legion opposes. This vast demonic army was created by the godlike being known as Sargeras to stop the Old Gods who work on behalf of the void lords, dark spirits that oppose the naaru - beings of both Light and Darkness.
Essentially, priests are the opposite of the warlocks, those who oppose the divine order of the Light and Void. Ironically, Sargeras' warlocks - as opposed to the priests - would be the ones with the ability to invoke the demonic forces of Light and Void because they don't oppose the disorder of Sargeras' demonic army and would be able to summon demons on behalf of the Legion. As such, if priests truly oppose the disorder of Sargeras' demonic army of demons, priests would be mages who invoke the Light and Darkness to control and banish demons.
A Clash of Faith
Between Light and Shadow
The bonds of magic shatter like broken glass in the grasp of an experienced priest. - Mass Dispel
Some priests pride themselves on pragmatism. They understand that light casts a shadow, that darkness is defined by light, and that true discipline stems from one’s ability to balance these opposing powers in services of a greater cause. While these priests possess many holy virtues to aid their allies, they also dabble in the dark arts to debilitate their enemies—always exercising immense discipline to keep themselves away from the brink of insanity. Many would say the ends justify the means; scriptures both virtuous and vile should be studied and understood to protect the congregation.
How you die can say a lot about how you lived. - Spirit of Redemption
After spending much of their lives in temples studying ancient doctrine, preaching the tenets of their faith, and pledging their full devotion to the divine powers they follow, the most adept priests leave their houses of worship to serve on the battlefield, as shepherd to flock. There, they use their holy powers to bless allies and mend wounds. And while most stay behind the frontlines to aid their comrades, these holy champions are also capable of smiting foes and carrying out sacred justice. They’re also morally opposed to the use of Shadow and Void magic—rather, they are exemplars of the incredible grace and power of the divine and the Light, and even death cannot fully stop their healing capabilities.
Victims of a shadow priest seldom remember why they're victims. - Mind Spike
The body need not be slain for a priest to exert command over the soul. - Deacon Markus Hallow
The Light in which many priests bathe is brilliant and effervescent, granting them immense divine power. But the brightest light casts the darkest shadow—and from within this blackness, a rival power dwells. Shadow priests fully embrace this opposing polarity, their faith equally resolute as their holy counterparts—but focused on shadowy magics and mental manipulation. Like all priests, they dedicate much of their lives to worship—but they derive their power from the Void, straying dangerously close to the domain of the Old Gods. To truly understand such ancient, corruptive influence is to be driven mad. This is the state in which these dark priests thrive, embracing insanity and feeding off of the minds of their opponents to reach terrifying new limits.