Originally, the reason for Superman's abilities was not explicitly detailed – other than stating Superman is an alien. However, as the Superman character developed over the years, DC writers attempted to provide real world explanations for the hero's super powers, settling on the idea that Superman receives his abilities from stored-up solar energy - via Earth's yellow sun. Where Kryptonians lived under the harsh conditions of a red sun, known as Rao, Superman's body is able to metabolize energy from Earth’s yellow sun (similar to how humans metabolize energy from their food) - then uses that energy to fuel his various super powers (with the added benefit of slowing the kryptonian's aging). Like most life forms, Superman can also store excess energy for later use – which is then used to fuel many of Kal-El’s powers
Super Strength, Speed, and Perception
Initially described as "more powerful than a locomotive and faster than a speeding bullet," Kal-El's super abilities have increased significantly over the years. Yet, Superman's strength, endurance, and speed, are derived from stored solar energy - providing fuel to his inherently dense molecular structure - allowing Kal-El to move with superhuman force (all without injury to himself). Still, for that reason, Superman's raw power is incalculable - since his strength and speed is not a uniform benchmark and can be diminished or amplified by other conditions and external factors – especially the amount of solar energy he has stored.
Kal-El has only been shown to possess telekinetic abilities on a few isolated occasions; however, it is largely accepted that Superman’s store of solar energy also affords him a bio-electric aura that allows him to manipulate electromagnetic fields – an ability that has come to be known as “tactile telekinesis.” Tactile telekinesis attempts to explain why Superman can pick up a jetliner by the nose without the entire airplane buckling from the pull of gravity on the tail-end (for example) - asserting that the hero was surrounded by a solar-powered telekinetic aura that engulfed anything he touched - resulting in both physical and electromagnetic field manipulation to evenly distribute force across an object through only one point of contact.
Certain versions of Superman also credit his "bio-electric aura" as a contributor to the hero’s invulnerability – as the bio-electric aura also surrounds objects and organisms in Superman's immediate vicinity, making it possible for Kal-El to protect Lois Lane, for example, from a deadly explosion without having to cover every square inch of her body. The strength and range of Superman's bio-electric aura varies but, in an extreme case, enabled the hero to survive a supernova.
Since Superman's powers are derived by absorbing and metabolizing solar energy then using that energy to fuel super strength, speed, and other enhanced abilities, one of the more literal examples of this process is Superman's heat vision - which allows the hero to emit stored solar energy as directed beams of focused heat through his eyes. The beams have varied in precision and strength throughout the years but have been shown to reach objects over a hundred feet away and, conversely, feature surgical accuracy - down to microscopic levels. Depending on the situation and intensity of the emission, Superman's heat vision can be invisible to the naked eye - allowing the hero to use the power, albeit sparingly, even when disguised as Clark Kent.
As indicated, Superman can also over-charge with solar power, and in modern versions of the character, a new evolution of heat vision was introduced: the "super flare." Using the same mechanics as heat vision, Superman can unleash a devastating attack on his surrounding environment - by venting the stored solar energy in every single one of his cells. The super flare is possibly the hero's most powerful ability but comes with a downside - expelling all of his stored up solar energy leaves Kal-El vulnerable and without powers, essentially human, for nearly 24 hours (the time it takes him to recharge his solar stores).