"How does it feel, knowing you helped me become the Prime Evil? For all your mighty deeds, all you really accomplished was unleashing me upon the world. Some savior you are, nephalem."— The Aspect of Terror(src)
The Aspect of Terror, Diablo's Herald was a demon under the banner of Diablo. It attempted to deny the Nephalem entry into the Silver Spire, appearing in the form of Leah and ambushing the Nephalem. Despite its efforts, it was defeated, and the Nephalem continued on their path towards the Lord of Terror.
The Aspect of Terror appears in Act IV of Diablo III. It is a Super Unique Terror Demon. As the Aspect of Terror reaches lower health levels, several other Terror Demons will come to its aid, and when those demons reach low health levels, several more appear. Killing him also summons a squad of lesser Terror Demons. This could get the fight out of hand. The Aspect of Terror also periodically vanishes, summoning Shadow Fiends in its place. He also has Fast, Jailer and Electrified affixes.
Killing it is not required for the quest, and one can even ignore Leah's ghost altogether.
Unlike the rest of the Aspects in Act IV, the Aspect of Terror will spawn regardless of the player's luck with the game's randomization factor in Campaign. In Adventure Mode, he may appear as a bounty in Silver Spire Level 2. In this case, he does not summon more Terror Demons.
Interestingly, he does not have Nightmarish affix, despite being the monster who would seemingly must have it.