The film introduces "atmosphere" as a co-dependent power source which confuses things for so many, in order to give Zod and his platoon a weakness of sorts. Having said that, for this film series the weaknesses, the additions and exclusions of how Kryptonians derive their power makes Superman more vulnerable, without using Kryptonite or a genius Lex Luthor yet! It gives more scope for future movies.
I really like Keen's (June27) explanation which reconciles this new "atmospheric" source of power for the film. To expand on Keen's explanation would be to consider any reference to the 'ship's atmospherics' as one that encompasses both Krypton's atmosphere as well as radiation from their native red giant star plus the ship blocking our Sun's radiation... perhaps the biosuits and breathers are the same except without the red giant radiation part, with their basic abilities such as strength, speed and invulnerability derived from their natural Kryptonian physiology as well as the Sun.
However, in introducing atmosphere as an addition source, they wipe out entirely the comic book lore that Clark is a living battery and his augmented powers are a direct result of this energy store and manipulation by his natural physiology. To reinforce the film idea that he is no longer a battery is the fact that his powers can be switched on and off quite easily.
Comics generally show his basic powers of speed, strength, invulnerability and perhaps flight are due to his Kryptonian physiology from being from a more massive planet (high G giving dense structure: skin, bones, muscle therefore strength and speed and invulnerability and maybe anti grav organs, harsh environment and weak solar radiation to give efficient organs such as eyes, skin, lungs etc...). Kryptonians are also highly evolved minds and another explanation used in comics of Clark's ability to fly would be a form of self-telekinesis.
The radiation from a yellow star is of a wider spectrum and perhaps more energetic than a red giant. Clark's extra abilities stem from storing this energy for years, augmenting his natural strength/speed as well as augmenting things that are also natural to humans - such as the senses. His heat vision in comics is the ultimate expression of this power stored. Comics use the fact that Clark like any battery can deplete his store of energy when cut off from a yellow star but because he has stored it for years it take a long time to both store and be used up. The solar battery explanation has been explained as one more evolutionary step that Kryptonians living on a darker world circling a Red Giant would evolved the ability to absorb and use everything their star had to offer. Hardly in the same league but most land vertebrates on Earth absorb UV light to produce vitamin D in order to absorb calcium for the skeleton.