In the Superman Returns film, Clark as a child leaps across the field back to the farm and crashes through the roof falling straight down face first. As he is about to hit the ground he pulls a Tom Cruise Mission impossible stop not hitting the ground and no wires. So obviously, in the lore, something was changed from the original explanation of it being him just leaping. There were several theories presented in the Superman comics lore through the years:
Lex Luthor once theorized that Superman had to stem from a gigantic planet with enormous gravity, where his species had developed natural anti-gravity organs to be able to function; on Earth, this would allow him to control his own gravimetric field in order to fly.
When making the cartoons, the Fleischer Brothers found it difficult to keep animating him leaping and requested to DC to change his ability to flying; this was an especially convenient concept for short films, which would have otherwise had to waste precious running time moving earthbound Clark Kent from place to place. Writers gradually increased his powers to larger extents during the Silver Age, in which Superman could fly to other worlds and galaxies and even across universes with relative ease.
It was originally stated that Superman's abilities derived from his Kryptonian heritage, which made him eons more evolved than humans. This was soon amended, with the source for the powers now based upon the establishment of Krypton's gravity as having been stronger than that of the Earth.
In John Byrne's original "Man of Steel" reboot of Superman, the position was adopted that most or all of Superman's powers were fundamentally psychokinetic in nature. This really made, and continues to make, an enormous amount of sense, explaining as it does things like why he gets strength and heat vision in the same power set, why his costume is as invulnerable as he is (he projects a PK barrier a little bit outward from his skin), and how he's able to do things like lift aircraft carriers without worrying about either his own leverage or whether the part of the thing he's holding onto has a millionth of the tensile strength necessary to be used as a lever to move the rest.
Different writers make different implications all the time, of course, but the psychokinetic model has continued to pop up over the years in a number of ways, such as in the case of Superboy, with his partial Kryptonian DNA, having as a power "tactile telekinesis" a phrase by DC's absolute determination to keep repeating it as often as humanly possible and then some.
