Snyder deserves no benefit of the doubt after BvS and it will be a long, long time before I can be said to be optimistic about this. But that said, the tone is a total 180 from BvS. There is more levity in this little bit of footage than in that entire movie combined. And in general everyone seems like less of a glowering a hole. It's a sign of hope. And I'm liking Ezra Miller from what I see here, even if that costume isn't my favorite.
They're essentially among the most powerful devices in the universe, used by the New Gods of Apokalips and New Genesis. They serve a variety of functions, from being the most super of super computers to opening Boom Tubes (wormholes) for transportation across the universe to accessing the power of The Source (the latent consciousness of the universe and the source of everything in existence). The original Cyborg was not enhanced with Mother Box technology, but the New 52 version was created when he was basically fused to a Mother Box. Since it looked like that's what happened to him in BvS and the Mother Boxes are going to the a significant part of Justice League, they're going with that version of Cyborg.