What is the halting problem? What does it have to do with self referential paradoxes?

Question

How do I make sense of this?
"So suppose I have a black box which can decide the halting problem, that is I can give it a program P and the box tells me if P will ever stop.

Using this I can make a program P' that works as follows:
Given a program P ask the box if P will stop.
If P will halt run forever.
If P will run forever, halt.
Last step, give P' as input to itself, if P' will run forever it must halt. "

I don't understand why there is a P' here? And why we have regular P and P'. I'm so confused.