Why did Neo have powers in the real world?

Question

In the Matrix, why did Neo have magic powers in the real world? For example,

(1) Those scenes where he blows up those robots purportedly with his mind.

(2) That one where he has no eyes but can see.

Answer 1

The main explanation I've seen, and that seems to be pretty official, was that the plug thing Neo has in the back of his head worked as a wireless device. Well, as you will read below, this isn't actually specified like this, but since the source speaks of the "brain becoming a wireless connection", it seems the safest thing to assume.

In any case, no magic is involved.

In the IMDB FAQ page for Matrix Reloaded, we see the question: Neo is able to have extraordinary powers inside The Matrix because he is The One, designated by the machines for equilibrium. What explanation does the movie give for Neo having his powers in the real world?

And the answer is (emphasis mine).

The answer is given in Revolutions. The machines in the real world are all connected to a "singular consciousness", the birth of Artificial Intelligence described by Morpheus in the original Matrix film. This consciousness is otherwise known as "The Source".

The machine connection is a remote one or some sort of wireless signal. Having touched The Source (i.e. - meeting with the Architect) and having the data needed to reboot the Matrix, Neo is at this point simultaneously in possession of his human brain but also connected to the singular consciousness. In other words, his is also now a wireless connection. Hence, the reason Neo says, "Something's different. I can feel them." The machines are all separate entities but all connected to this one ("The Source"). Now Neo is as well.

He is thereby able to harness this power and stop the sentinels. However, Neo wasn't ready to handle the signal surge and collapsed in a comatose state, no longer in control of just where this wireless signal would be directed. The signal (Neo's residual self-image) is then captured and held in a program limbo derived from the Source but undetected as an existing realm, so to speak. This limbo (the Train Station) was created by the Trainman, a program in service to the Merovingian.

This connection forged by Neo's visit to the Architect and his subsequent decision to return to the real world made him, unknowingly, unique. Neo became simultaneously human and machine in a sense. This would ultimately put him in the position to negotiate for peace between humans and the machines. This, as the story unfolded, is exactly what happened.

Answer 2

If you want to force an explanation,the idea is that Neo is like an virus inside matrix same as one virus would be on your computer,but when Neo is unplugged/your pc powered off it can't pose any threat.

But if the virus was so good,and your hardware(motherboard BIOS) poorly built/programmed...the virus could theoretically take control of your motherboard,and next time you boot up your PC it could overclock its voltage until it burns out.

This could partially explain how he would destroy the robots,and seeing the machines would be just your windows recognizing your new USB keyboard however windows won't run on powered off pc so they can't recognize anything but on the other hand Neo,unlikely the windows had an advantage of existing in both worlds(software/hardware).

He couldn't just beat up the robots like he did in matrix since there was much more effort needed,he had to implement the whole new hardware part to his strategy,which would also explain why he didn't do it more often.