When Henry James wrote The Turn of the Screw, he was careful to leave the actions of the ghosts Quint and Jessel unspoken. Their relation to young Miles and Flora is never detailed, nor is their ultimate goal any less a mystery to the readers as it is to the characters in the story. A lot of ink has been spilled over the past hundred years because of this — some believing the ghosts to be child molesters, some forsaken lovers, some as wanting to possess the children in an effort to return to this world — and most of it misses the point entirely. They attempt to assign mortal logic to extra-mortal beings. They fail to understand the essence of absolute evil.
Iago. Judge Holden. Morgan le Fay, to a lesser extent. Three characters from three wildly different genres of fiction, and yet they all serve much the same purpose to the reader. They are conniving, clever, able to be bargained with but never safely. Because their motives are never known, their potential is functionally infinite: far from being evil for the sake of evil, their characterization hints at a greater purpose beyond the reader's comprehension.
Another good example of this would be Kefka, the psychopathic, nihilist nemesis from Final Fantasy VI. Kefka is not a tragic villain, to be pitied. Nor is he simply a lunatic murderer; there is intellect and design in his machinations throughout the game. But his greatest strength as an enemy is that he is never given a clear motive for what he does. Even after killing millions, ascending to godhood, and nearly destroying the world itself, his purpose remains unknown. The player defeats him, and is left with a bitter thought to comfort them: what caused this? Could it happen again? Could it happen to me?
Absolute evil is a hard-but-rewarding topic to confront in your game. If the evil character is too transparent or emphatic, they can come off as nothing more than an agent of chaos. Conversely, if the evil character is too strong and unknowable, they become Lovecraftian: a force of nature, outside of mortal influence. That's no good either. If you're doing absolute evil right, your PC's — and the players themselves — should be anxious. They should feel like they've only been given a piece of a grand puzzle, or like they've been thrown into the deep end without knowing how to swim. You've brought something upon them that is so unlike everything they've faced so far: beasts driven by instinct, rulers lusting for power, mad wizards seduced by curiosity. Your players should be asking themselves and each other the following questions, without clear answers:
What is this creatures purpose?
What is this creatures next move?
What is this creatures end goal?
How powerful is this creature?
Can this creature be stopped?
Can this creature be bargained with?
Once they've started asking, the hard part of your job as a DM is done. Now, all you need to do is resist the temptation to answer them.
If your absolute evil is undead, demonic, or otherwise divorced from the mortal coil, then their plan may simply be too complicated for mortals to understand. In D&D, as in real-life, there is an upper limit to intelligence; perhaps your characters can no more comprehend the machinations of a demilich than a guinea pig can comprehend calculus.
If your absolute evil is human/elven/dwarfen/other intelligent mortal creature, then its motives need not be explained BUT they should be hinted at, in addition to other, unrelated motives. The party finds out that the witch that's been casting a blight on the land was once scorned by a lovely princess, and sets out to reunite them... upon which the witch casually murders her in cold blood and mixes her corpse into the pudding. You must keep them guessing, but never fall back unto mindlessness! A creature without a motive is boring.
In playing the villain, be cagey and strange. Embrace the chaos that invariably stems from PC behavior. Make them fight for every inch of ground, then take it away from them in a cunning reveal that what they were doing was exactly what you planned all along. Toy with them: you are all of the worst aspects of Littlefinger and Strahd combined, an unholy amalgam of every conniving little shit that ever ruined your day in real life. Gloat, as loudly and often as you can. If the PCs don't hate you — personally, as a living (or nonliving) creature, if they don't crave your destruction not for its practical benefits but just because you are too monstrous to live — then you have failed.
A good absolute evil can cause a PC to lose faith in themselves. A great absolute evil can cause a PC to lose faith in the world.