Darkseid's single-minded search for the Anti-Life Equation makes him one of DC Comics' most evil villains. As the ruler of Apokolips, a hellish planet mired in violence and hate, Darkseid sees the Anti-Life Equation as the ultimate way to achieve his goal: to destroy free will in the universe. While the Anti-Life Equation has been defined in numerous ways since Jack Kirby first created it in his Fourth World Saga, Kirby's original intention for it casts Darkseid's ambitions in a starkly human light, and recalls antiwar sentiments of the 1960s.
Kirby originally created the Anti-Life Equation in his Fourth World Saga, which spanned the titles Forever People, Mister Miracle, New Gods, and Superman's Pal, Jimmy Olsen in the early 1970s at DC Comics. Over the years, the Anti-Life Equation has evolved to contain specific elements, but its core purpose has changed little. The Anti-Life Equation, at its most basic, would give whoever possessed it the power to instantly control the minds of anyone around them. The concept of "Anti-Life" to Jack Kirby is essentially the destruction of free will, of people's ability to both make their own decisions and change for the better. For Kirby, the death of one's ability to choose their own path equals the death of them as a human being.
Originally, however, Jack Kirby intended the Anti-Life Equation to be something much more metaphysical. The book, Old Gods and New: A Companion to Jack Kirby's Fourth World by John Morrow contains a selection of an interview with Kirby's assistant Mark Evanier, where he states Kirby's original idea for the Anti-Life Equation:
"The plan Jack had for the Anti-Life Equation was that it didn't exist, at least not in the form Darkseid believed. Darkseid was chasing something he could never have. Whereas Darkseid perceived it as a weapon, it was a spiritual goodness that exists in every religion and every people... And it's something which, if Darkseid got his hands on it, he'd have a very powerful concept in his hands, but nothing he could ever use for conquest. I envisioned, or maybe Jack told me this, a scene with Darkseid finally realizing what the Anti-Life Equation is and screaming, 'I can't use this! This is of no use to me!' He'd killed hundreds of thousands of soldiers, and spent billions of dollars to get his hands on the ultimate weapon, and he discovered the ultimate weapon was, 'Thou shalt not conquer.'"
Jack Kirby's Original Intention For The Anti-Life Equation Is A Radical Statement On Darkseid's Evil.
This version of the Anti-Life Equation underscores the strong antiwar and anti-imperialist themes in Kirby's Fourth World Saga, most prominent in Forever People and New Gods. By making the most powerful weapon in the universe a deeply anti-imperialist idea ("Thou shalt not conquer"), rather than an object, Kirby imbues the Fourth World Saga with a sense of contemporary urgency. This sentiment recalls the message of popular antiwar songs from the 1960s like "One Tin Soldier," which told a story similar to Darkseid's search for the Anti-Life Equation. Given that Kirby was a Jewish American veteran of the Second World War who fought against Nazi Germany, his original vision for the Anti-Life Equation reflects his attempts to grapple with evil in the modern world. This idea was eventually brought up in a later New Gods series in issue #28 by Mark Evanier, Rick Hoberg, Frank MccLaughlin, Steve Montano, and Charles Barnett III, where the Source described the "essence" of the Anti-Life Equation as, "There is no Anti-Life. There is only Life."
Although the Anti-Life Equation was later revised by Jack Kirby, its original meaning emphasizes that the greatest power in the universe is Life, rather than Anti-Life. Kirby's experiences with war led him to believe that life is worth living, and isn't fundamentally meaningless like Darkseid believes it to be. The Anti-Life Equation has continued to shape the course of the DC Universe, so it's not totally out of the question to imagine that Jack Kirby's original intention for it with Darkseid could someday return.
Source: Old Gods and New: A Companion to Jack Kirby's Fourth World by John Morrow