"Look, up in the sky! It’s a bird! It’s a plane! It’s Superman!” Everyone knows this quote about the Man of Steel, but what most people don’t know is how he’s able to get up in the sky with the birds and planes in the first place. The answer, much like the character himself, has changed over time.
The DC comics icon was first created way back in 1938, and while the original version of Superman had some of the silliest, craziest, and altogether dumbest superpowers imaginable, flight actually wasn’t one of them. Back then, Superman was only able to “leap tall buildings in a single bound.” He couldn’t stay suspended in mid-air or shoot off into space; no matter how high he jumped, he’d eventually have to come down. However, Superman was given the ability to fly a few years later... though the reason behind the change was a logistical one.
Animators for the 1940s Superman cartoon found that they were wasting a lot of time animating Superman jumping to and from locations. They filed a request with DC to change his power from simply leaping to full-on flight. DC agreed and Superman has been flying around ever since. But what’s the explanation for Superman being Superman being able to fly in the comics themselves? After all, "Man of Steel" doesn’t exactly sound very aerodynamic. The reason for flight, like most of his other powers, has to do with his Kryptonian biology. With a twist.
Superman’s powers - his strength, speed, heat vision, everything - are derived from Earth’s yellow sun, which is more nourishing for his Kryptonian cells than the red sun of Krypton. But the color of the sun isn’t the only thing different about Earth. Krypton’s gravity was much stronger than Earth’s, so much stronger that Kryptonians had to evolve to develop anti-gravity organs. These organs made it possible for Kryptonians to move around on Krypton without being crushed by the intense gravity. But on Earth, which has both weaker gravity and a kinder atmosphere, they can basically resist gravity so strongly, they defy it altogether. And while the storytellers since then have called out the anti-gravity organs to greater or lesser degrees, the overall effect on Superman's body is the same.
Even as recently as the movie adaptation Man of Steel, when Superman prepares to unleash the full potential of his alien body, causing the snow and stones around him to start to float. How? Just as in the comics, he’s essentially altering the gravity field around his body to enable himself to fly. This all goes to show that Superman can conquer any challenge - even one presented by a physical problem with his animation. It’s probably for the best that DC agreed to just have him fly - imagine all the property damage from Superman just jumping around Metropolis instead.