How do the Avengers' superpowers actually work? Well, not like actually, because they couldn't exist - but are the Avengers' powers explained in the movies? The short answer: Yes, they're explained in all the pseudoscience jargon the MCU scribes could muster.
The Avengers have some incredible powers, like Scarlet Witch's ability to move objects with her mind, or Ant-Man's ability to shrink himself down to any size. But, those abilities both work a little differently than the average viewer is probably thinking while watching. The explanations for the Avengers' powers given throughout the films are definitely more than a little convoluted and contain more than a couple of references to the Tesseract and other Infinity Stones as sort of a "we don't have to actually explain any of this to you" get-out-of-jail-free card.
With that said, the Scarlet Witch's secret ability to alter reality - and finding the line between where Thor's powers end and his hammer's begin - make looking into this more than a little interesting.
Bruce Banner became the Hulk after accepting a military contract from the US government to recreate the Super Soldier Serum that turned Steve Rogers into Captain America. During the process, Banner accidentally exposed himself to gamma radiation and gained the ability (read: curse) to turn into the Hulk whenever he gets angry.
Banner's transformation occurs whenever an "electric pulse generated on the amygdala increases the gamma radiation of Bruce's cells." The cells in Banner's body absorb the gamma, causing him to rapidly increase in size. When the anger wears off, a chemical reaction occurs that creates a "myostatin primer." The Hulk turns back into Banner, and the muscles and energy are dissipated.
The Super Soldier Serum that Steve Rogers ingests in Captain America: The First Avenger is the United States' attempt to turn regular human beings into perfect soldiers. Luckily for them, it works perfectly on Steve Rogers, transforming him into Captain America (immediately before they lose the serum forever).
The serum does two things in particular. It enhances the subject in all ways: strength, speed, agility, reflexes, intelligence, etc. Along with those very noticeable enhancements, it also cures the subject of all ailments. If they had cancer cells in their body, they don't now. The serum enhances everything in the person who took it, including personality traits. The Red Skull became more evil and twisted after taking it, whereas Rogers became even more of a hero.
Ant-Man has two main powers: He can manipulate his size, and he can talk to ants. The first of these powers, the size manipulation, occurs thanks to Pym Particles developed by Hank Pym. These are extra-dimensional particles that are able to be harnessed in a way that increases or decreases the extra space between atoms in the body. So, it's not really Ant-Man that is shrinking down, it's just that the atoms are getting closer.
Ant-Man can communicate with ants thanks to his helmet's ability to send EMPS. Basically, the helmet can use electromagnetic waves to "stimulate the olfactory nerve center and pheromones of insect-sized organisms."
While it is immediately apparent that Quicksilver can run fast, that's not the full extent of his powers. Pietro was a refugee who volunteered to undergo Hydra experimentation alongside his sister to get revenge for the demise of their parents. This resulted in the two of them gaining incredible powers.
A normal human processes the happenings around them at a consistent speed, unchanged by how fast they are moving. This is not the case for Pietro. Pietro was able to accelerate his perception so that while he was moving at super speed, he could react in super speed. This resulted in him seeing the world around him in slow motion, allowing him time to plan his maneuvers and act them out in fractions of a second.
The Scarlet Witch was radicalized and experimented on by Hydra, who used the Mind Stone to give her incredible powers. She appears to have telepathic and telekinetic abilities. However, what she is really doing is altering reality by manipulating molecular polarity.
As she harnesses these reality-altering powers further, as shown in WandaVision, the extent of her abilities is finally revealed. She is a great deal more powerful than anyone realized back in Age of Ultron.
The Vision is a synthezoid, meaning he is a hybrid between organic and inorganic matter. His body is made out of a little bit of organic tissue and a little bit of vibranium, and uses a lot of help from an Infinity Stone to make it all come to life.
To discuss Vision's powers, it is necessary to discuss the Mind Stone. As Wong describes it:
From the dawn of the universe, there was nothing. Then... boom. The Big Bang sent six elemental crystals hurtling across the virgin universe. These Infinity Stones each control an essential aspect of existence.
Basically, this stone controls one of the core tenets of the universe, specifically, the mind. When embedded into Vision's head, it works to give him sentience, turning him into a living being with incredible powers.
The Infinity Stones have complete control over reality itself, so when Vision is wielding the Mind Stone, even if it is just one stone, a pesky wall is no match for it. Vision can phase through walls with no problem, fly, or even shoot energy projections out of the stone.
