In Zack Snyder's Justice League, the scream Superman (Henry Cavill) emits when he's killed by Doomsday is the trigger that awakens the three Mother Boxes. How this works ties into Zack Snyder's mythical approach towards Superman, Darkseid, Steppenwolf (Ciaran Hinds), and the villains from Apokolips in the Snyder Cut.
Superman laid down his life to stop Doomsday in Batman v Superman: Dawn of Justice. As the Man of Steel plunged the Kryptonite spear into Doomsday, the Kryptonian monster drove his spiked hand into Superman's heart. Zack Snyder's Justice League opens on this pivotal moment, adding the powerful scream from Superman in his death throes. The sonic boom of Superman's anguish reverberated across the entire planet, but the most significant after-effect was the Mother Boxes hearing Superman's scream. From their disparate location in Atlantis, Themyscira, and Cyborg's apartment, the three Apokoliptian Change Engines "woke up" from thousands of years of dormancy, signaling to their master that Earth was safe to invade, which is what brought Steppenwolf back to acquire the Change Engines. Once he collected two of the Mother Boxes, they told him that the Anti-Life Equation was hidden on Earth.
Zack Snyder explained how and why Superman's scream activated the Mother Boxes during his live stream watch party for Batman v Superman last year. According to the director, Superman's death scream was "an Excalibur moment... You hear the scream echo... That sound goes out into the world, echoes across the globe, and if there were sleeping Mother Boxes on Earth, that sound would wake them up." Once awake, the Mother Boxes relayed the crucial information of Superman's death back to Steppenwolf: Without the Kryptonian to protect the planet, the Earth was safe to invade. Steppenwolf later reiterated this belief to DeSaad: "No protectors here. No Kryptonian. No Lanterns. This world will fall like all the others."
It can be assumed that, even in their dormant state, the Mother Boxes were able to sense major threats to Apokolips. Thousands of years ago, Darkseid's first invasion of Earth was repelled by an alliance of Atlanteans, Amazons, the Greek gods, and humans. By Steppenwolf's own words, the only beings that the Mother Boxes recognized as protectors of Earth to be feared were Green Lanterns and Superman from Krypton. However, in the present day, the Amazons and the Atlanteans are isolated, the Greek gods are gone (despite the presence of Wonder Woman, who killed Ares in 1918), and there's no Green Lanterns on Earth. Once Superman died, the last true impediment for Apokolips to invade was removed from the equation.
There are certainly some questions created by the Snyder Cut's mythology, like why Steppenwolf or Darkseid didn't return to Earth in the thousands of years before Superman was born, or why the other powerful super-beings on the planet like Wonder Woman, Aquaman (Jason Momoa), or The Flash (Ezra Miller) weren't considered threats by the Mother Boxes. Then again, it was clear once Superman was resurrected that his sheer power was on an entirely different level than even Wonder Woman, and the Man of Steel completely outmatched Steppenwolf. The Justice League working together not only humbled Steppenwolf but they boldly sent his decapitated corpse through a Boom Tube to land at Darkseid's feet, sending the Lord of Apokolips a definitive message.
The way Zack Snyder's Justice League opened on Superman's death scream waking the Mother Boxes powerfully conveys Superman's status as a god-level being himself. It's more impressively mythic than how the Mother Boxes came online in Justice League's theatrical cut, where they were still awakened by Superman's death, which they just managed to sense somehow. By having Superman's death scream echo throughout the world, Zack Snyder's Justice League delivered a memorable visual and a definitive motivator for the Mother Boxes to awaken that sets the epic story into motion.
