WARNING: The following article contains spoilers for Justice League, in theaters now.
In DC Comics, Mother Boxes are created by Apokoliptian scientist Himon using the fairly-unexplained and mysterious Element X. They're typically found on New Genesis, home of the New Gods, and even these highly powerful beings don't truly understand their true nature and origins. Mother Boxes are sentient, portable supercomputers that possess impressive powers, including teleportation (by manifesting boom tubes) and energy manipulation. There is also such thing as a Father Box, an Apokoliptian version of a Mother Box, which could well materialize as Warner Bros.' DC Extended Universe continues to expand, but for now, the focus is solely on the former piece of technology.
Mother Boxes are a huge deal in DC Extended Universe. In fact, they're the driving force of the Justice League, ultimately giving Batman and Wonder Woman the need to recruit The Flash, Cyborg and Aquaman - and it's partly why, and how, the League is able to resurrect Superman. One of the three Mother Boxes currently on Earth was briefly shown in Batman v Superman: Dawn of Justice, but despite being limited to a camp role there, their importance to the DCEU can't be overstated. The whole reason the Justice League unites is to stop Steppenwolf, the self-proclaimed "End of Worlds." The villainous extraterrestrial being invades Earth multiple times throughout the movie to gather the Mother Boxes.
Upon his investigations of Parademons and his numerous travels to recruit "warriors," Bruce Wayne continues to notice the same symbols: three boxes. It takes a long talk with Diana Prince, better known as Wonder Woman, for him to finally find answers. Steppenwolf had previously attacked Earth, armed with three Mother Boxes, with plans to take over the world and completely renovate it.
So, where are the Mother Boxes located? Well, it's kind of an epic story. When Steppenwolf invaded many years ago, the forces of the Atlanteans, Amazonians, humans, and other beings (such as Zeus and a Green Lantern) come together to save the planet. Overpowering the invaders, they sent the aliens back to their own dimension. It's decided that one Mother Box will be securely kept in Atlantis, another in Themyscira, and the final one hidden underground by humans.
When the three Mother Boxes converge, they form what's known as the Unity - which is mentioned multiple times throughout the film, but never fully explained. What's known is that the Unity is a force of power that Steppenwolf and the forces of Apolokips use to invade and take over planets. You can see how this is a problem when the antagonist arrives on Earth once more.
The Mother Box that was in the possession of the humans is unearthed and eventually finds it way to S.T.A.R. Labs, where Cyborg's dad Silas Stone ends up with it. When Victor Stone is in a severe accident and his life is on the line, a Mother Box is used to help breath life into his new technology-infused body. The Mother Box leaves a lasting effect on Cyborg, allowing him to have somewhat of an understanding on what they are and what they're capable of.
While it's not clear if New Gods other than Steppenwolf will eventually show up in the DC Extended Universe, it's likely that we haven't seen the end of the Mother Boxes, at least. There's a chance Darkseid will decide to take matters into his own hands and decide to assemble the Mother Boxes himself, a development that would likely be the focus of a Justice League sequel.
Available now in theaters, Justice League stars Ben Affleck as Batman, Henry Cavill as Superman, Amy Adams as Lois Lane, Gal Gadot as Wonder Woman, Jason Momoa as Aquaman, Ezra Miller as The Flash, Raymond Fisher as Cyborg, Willem Dafoe as Vulko, Jeremy Irons as Alfred Pennyworth, Diane Lane as Martha Kent, Connie Nielsen as Queen Hippolyta, Amber Heard as Mera and J.K. Simmons as Commissioner Gordon.