The Justice League is comprised of the most iconic heroes of all time, but attempting to give an explanation for Justice League powers can actually be pretty complicated. Superman has been around for over 80 years, but even with all that time, writers haven't developed the most logical reasoning for how he can fly. Still, the various explanations given for the powers featured in the DCEU films were delightfully laden with sci-fi jargon, and they're a ton of fun to analyze.
So, how do the Justice League superpowers actually work? How are the Justice League's powers explained to make an iota of sense? To put it frankly, even the most basic DC powers don't work the way the average viewer would assume. Thought Superman could fly? Well, sort of, but it's more complicated than that. Under the impression Flash is fast? Well, it's not the Flash who's fast; he's actually pulling in power from a different dimension. The Justice League might be the world's strongest heroes, but that doesn't mean their powers have the world's strongest explanations.
The Superman radio program, responsible for much of the classic Superman lore, described the Kryptonian as being able to leap tall buildings with a single bound. That's right, back in the day, Superman couldn't actually fly. Superman didn't fly until a new creator took over the comic, apparently didn't do their research, and just assumed Superman could fly. The blue boy scout's flight was later popularized thanks to early cartoons, where animators found it easier to draw him flying without having to animate a leap.
Clark Kent's powers come from the difference between the stars orbited by Earth and Krypton. Krypton orbits a much more powerful red star, whereas Earth orbits a weaker yellow star. On Earth, Clark Kent's Kryptonian DNA responds in strange ways to the weaker star and grants Kent incredible abilities he uses under the moniker Superman. Chief among those abilities is Clark's power to manipulate gravity around him, allowing himself to fly through the air. Viewers can see this gravity manipulation in Man of Steel, where before Clark achieves liftoff, the pebbles around him begin to rise into the air.
The Flash moves at super speed. This power seems simple, but the reality behind how it works is surprisingly complicated.
Barry Allen gained his powers through a fortuitous mishap. Barry was struck by lightning at the same moment that chemicals spilled on him, and this occurance made him a conduit of the Speed Force. The Speed Force is an energy field from a different dimension, and Barry can pull from it to move at super speed. So, unlike Wonder Woman and Aquaman, who can move quickly due to their actual bodies, it would be incorrect to say Barry Allen himself is technically fast. It's the work of the Speed Force propelling Allen at incredible speeds.
Aquaman is an oft-mocked character from DC Comics, but no one is laughing at the hulking Aquaman portrayed by Jason Momoa. And, no, Aquaman isn't just powerful in the ocean, either.
Aquaman has a combined human/Atlantean physiology that grants him superhuman strength and durability. Aquaman also possesses a Wolverine-like healing factor and only requires a matter of hours to heal from heavy injuries. He may not be quite as strong as Superman, but he can match Wonder Woman in strength, agility, and speed. Not to mention his considerable underwater abilities, as well.
After the wizard Shazam chose the young Billy Batson as his champion, Billy needed to simply utter the name "Shazam" to turn into a jacked adult hero. Billy's considerable physical upgrades were more prominently displayed while testing his powers, but that's not the only part of him that received a boost. While in the form of Shazam, Billy also possesses the Wisdom of Solomon. The Wisdom of Solomon means Shazam has a genius-level intellect, and all he has to do is willingly tap into it.
Shazam notably used this ability to defeat Dr. Sivana. Shazam wisely coaxed out the last remaining sin from Sivana's body, causing Sivana to lose all of his abilities and allowing Shazam to quickly defeat the mindless sin.
Victor Stone, AKA Cyborg, became more robot than man after he survived a terrible car accident. Cyborg's father was unwilling to watch his son perish, so he preserved his boy and used his considerable technical abilities to create a new robotic body for Victor to inhabit.
In Justice League, Cyborg's powerset was a little less clear-cut than, say, Superman, but that's for a good reason. Cyborg's entire being is in a constant state of self-modification. Basically, Cyborg's body troubleshoots itself and provides him with new abilities should he need them, such as suddenly discovering he's capable of flight or turning his hand into a plasma cannon.
Wonder Woman is the child of an Amazon and one of the Old Gods - specifically, Zeus. This gives Diana incredible abilities, not just when compared to humans but even to other Amazonians. Wonder Woman is obviously a brilliant fighter and possesses heightened physical abilities. But she also has a few powers that are a bit harder to understand, like the powers provided to her by her magic bracelets.
Through the use of her bracelets, Wonder Woman can release blasts of energy from the Old Gods. When Wonder Woman clashes these bracelets together, a massive explosion of energy is projected, decimating anything in its path.