Following the appearance of concept art from Zack Snyder's Justice League on Reddit indicating that a young Darkseid came to Earth in the past, the director has hinted as to what exactly he came for, with all fingers pointing to the Anti-Life Equation.
The art showcased Darkseid trying to invade Earth, a different take on the scene when Steppenwolf and his Parademons fought off the alliance between the Atlanteans and the Amazons, and now we know why. Snyder, on the Vero social media platform, indicated he was searching for something that would make him "unbeatable."
In DC lore, Darkseid's search and eventual use of the Anti-Life Equation has been one of the universe's greatest threats, as it results in all life submitting to the villain's will. It was introduced in Jack Kirby's Fourth World setting in the 1970s and would have actually provided a solid reason for the overlord himself coming to Earth.
The final cut, co-directed by Joss Whedon, had Steppenwolf failing in his previous invasion of the planet, and then returning to claim three Mother Boxes. However, a flashback with Darkseid would have certainly made it clear why the forces of Apokolips wanted to claim Earth for their own, as it would have provided their master the key to enslaving all life in the cosmos.