Neo isn’t actually human. He’s an organic DNA program, designed by a series of programs within the Matrix and synthesized by the Machines as part of an initiative called The Human Interface Program. Officially speaking, the machines wanted to create these genetically engineered humans because they wouldn’t be able to jack out of the Matrix. The machines wanted to functionally create “wifi people” who couldn’t simply be unplugged. No unplugging, no escapes. There was also a hidden agenda- a series of rogue programs within the Matrix called the Oligarchs manipulated these events to push the HIP agenda because it would allow them to exit the Matrix and enter human bodies.
The problem with this plan? The machines didn’t intend for Neo to be The One. That was an accident. The cycle of the one is functionally random- the programs in charge of creating the one were not privy to the details of the Human Interface Program. Because Neo had the capacity to manipulate code at will, he was able to jack in and out of the matrix without actually plugging in. Neo was a walking WiFi hotspot in the real world, with all the administrative tools. When he shuts down machines, he’s using his “Wifi connection,” to shut down the connections machines have to their power source, which powers them over-the-air.
Neo’s part in the Human Interface Project is also how Smith is able to leave the Matrix and enter into Cain’s body in the sequels. After Neo corrupts and “destroys” Smith in the first film, Smith’s code repairs itself but is tainted by Neo’s own code. Smith gains the ancillary HIP privileges to come and go from the matrix.
That covers the big stuff, as short as I can explain it.
Th Rabbit holes goes very deep…
It’s the idea that the small percentage of humans who reject the matrix are placed in the outer matrix that simulates a shitty ‘real world’ that they can fight all-powerful robots in. But it goes deeper. It’s been argued that the multiple iterations of the matrix that the Architect speaks of aren’t because the machines keep resetting the matrix, but because HUMANS do.
In this theory there are many levels of matrices within one another and at some higher level matrix there are humans controlling and resetting Neo’s matrix and killing all the humans in the ‘real world’ matrix that Neo thinks is real life. This is how his power can spill over into the ‘real world’.
Why are humans at a higher level doing this? Because above them is an even higher level matrix (possibly reality or just another level of simulation, though at this point it really doesn’t matter) where machines exist that the humans are enslaved by and trying to destroy. So they create a simulation of the reality they know with the hope of creating an entity that can destroy their machine oppressors. They make God knows how many layers of matrices, but at the bottom is a ‘real life’ matrix and a ‘matrix’ matrix (the ones in the films) and they keep trying different iterations in the hopes of evolving a Neo to the point where he can transcend the fake matrices they’ve created and filter all the way up to the top of their existence where he can burst through the ceiling of their reality and rend the machines that control them into tiny bits of either metallic or logical dust.
Or it’s actually machines at the top who make this simulation just as the NSA would simulate a cyber-attack in order to stop the real enslaved humans in the real matrix from ever getting out.