Recently appearing Zack Snyder's Justice League, the Anti-Life Equation is the ultimate weapon of Darkseid, but rather than being a mysterious force, it's one that's well documented in DC Comics. In the DCEU, Darkseid has yet to acquire the Anti-Life Equation, meaning that it's portrayed more as a mythic treasure rather than as something anyone could access, but the comics have gone into far more detail about the exact formula behind the Equation, what it can do, and even how it can go wrong.
The Anti-Life Equation, created by Jack Kirby, was introduced in Forever People #5. The comic was part of Kirby's Fourth World Saga, which explored characters like Darkseid and the New Gods. The being who wields the Anti-Life Equation is said to have full control over any person subjected to its formula, while anyone subjected to the Equation has no control over their actions and is described as not being truly alive. While the Anti-Life Equation exists as a mathematical formula, this is only its substance on the regular plane of existence. The New Gods exist at a higher level of abstraction than humans, and so what appears as a 'formula' on Earth is merely the expression of an invasive concept capable of influencing reality itself.
Darkseid didn't originally possess the Anti-Life Equation in the comics, and engaged in a hunt to retrieve its disparate parts. Despite running into several dead-ends in discovering and implementing the formula, Darkseid continued his search for Anti-Life and eventually managed to retrieve it, adding together many aspects of human emotion to create a feeling of endless hopelessness. It's the ultimate way to manipulate people as their minds become so clouded in despair that they accept total control. But while this horrifying process sounds mystical, the Anti-Life Equation has a very direct and specific expression as a mathematical formula, given in Seven Soldiers: Mister Miracle (from Grant Morrison, Pasqual Ferry, Billy Dallas Patton, Freddie E. Williams II) as loneliness + alienation + fear + despair + self-worth ÷ mockery ÷ condemnation ÷ misunderstanding x guilt x shame x failure x judgment n=y where y=hope and n=folly, love=lies, life=death, self=dark side.
Traditionally, this formula is written in alien symbols which manifest themselves around the Equation's user, signalling their connection to the extra-dimensional concept on which the formula actually draws. By speaking the full formula, Darkseid can implant the Anti-Life Equation into anyone's mind, though some heroes like Mister Miracle have been able to overcome it. Any being infected with the Anti-Life Equation is given the mathematical certainty that there is no hope in life and that freedom is a futile concept, with Darkseid in particular planning to bend the entire universe into becoming not his servants - as even that would imply some autonomy - but an extension of his will and being. In Final Crisis (from Grant Morrison, J.G. Jones and a host of other creators) Darkseid asks Superman, "What will you do when your friends, your enemies, your lover, are all Darkseid? ... One will. One life that is Darkseid. Will you be the enemy of all existence, then?"
Due to its nature as the mathematical expression of a larger idea, the Anti-Life Equation can manifest differently than Darkseid's intended use, and some characters have even tapped into its powers by accident in order to gain temporary control of others. 2019's DCeased (from Tom Taylor, Greg Capullo, and FCO Plascencia) saw a corrupted version of the Equation spread across the internet, causing a galaxy-wide outbreak that effectively turned its victims into violent zombies rather than the thralls of any one villain.
Expressing the Anti-Life Equation as a mathematical formula makes its cold, ruthless application all the more apparent, and many comic fans know the hugely influential formula by heart. Unlike in Zack Snyder's Justice League, the Anti-Life Equation in the comics is no mystery, and Darkseid's quest to master and disseminate is what makes him the comics' most terrifying villain.