The Mother Boxes have always played substantial parts in the comics, but they play an even bigger role in the movies, and here's exactly why.
Spoilers incoming for Justice League, so if you haven't seen the movie yet you've been warned.
The Mother Boxes were first seen in Batman v Superman: Dawn of Justice, specifically the one held by the humans. That box can be seen in the footage that Batman
Early on in Justice League, a flashback is shown depicting the great battle fought on behalf of Earth. Steppenwolf, a general of Darkseid, attempts to take over the planet, invading with his army of Parademons. He has brought three Mother Boxes with him, which when united form the Unity. Unity is the engine so to speak that has the power to transform a planet, and for Steppenwolf (and presumably Darkseid), the goal is to turn these planets into the image of Apokolips.
For those who don't know, Apokolips is the planet under the tyrannical rule of Darkseid. It's not a very friendly place, but being greeted at the door is the last thing on your mind when a planet looks like a hellish landscape filled with fire and lava-like geysers.
Steppenwolf's goal is to have Earth meet the same fate, and it takes the combined forces of the Amazons, Atlanteans, Green Lanterns, and humans to drive him back. They force him to retreat, and in the process, he has to leave his Mother Boxes behind.
As a precaution, the armies of Earth separate the Mother Boxes and keep them spread out across the planet. One is in the Amazon's possession, while one is in the vault in Atlantis. Another is held by the Humans, who bury it so others can't be tempted by its power.
That last one ends up being unearthed in a special scene on the Wonder Woman Blu-ray, retrieved by Etta Candy and the remaining group from the film, paving the way for Cyborg's creation.
Justice League is in theaters now.