The stories spring from a meeting Trump had with South Korean officials. They told Trump that the North Korean leader would like to have a face-to-face meeting with Donald Trump, and that the North Korean leader said he would be willing to discuss denuclearization.
Trump, impulsive as ever, went off half-cocked and announced to the press that he would be willing to have such a meeting. He then told the press that the North Koreans were willing to give up their nuclear weapons. He even had his press spokesman, Sarah Sanders, repeat that in a press conference -- although she seemed to walk back Trump's willingness to meet by saying certain "concrete" steps would have to occur before a meeting could take place.
Did North Korea really say it would be willing to unilaterally give up its nuclear weapons? No! They said they would be willing to discuss denuclearization. Isn't that the same thing that every nuclear power has said (including the United States)? They have all talked about a dream of a world without nuclear weapons -- but none of them have said they would unilaterally give up their nuclear weapons. And neither has North Korea.
No nation that has acquired nuclear weapons has been willing to give them up -- and anyone who believes North Korea will be the first to do so is living in a dream world. North Korea is NOT going to give up its nuclear weapons.
They did say they would be willing to stop testing for a while to have a one-to-one meeting between Kim Jong-Un and Donald Trump. This is not surprising, since they already have the bomb and the missile delivery systems. Why would they want this meeting (since they are not doing to give up their nuclear weapons)? For propaganda purposes. It would allow them to pose as an equal to the United States, and in their eyes, would enhance their importance.
I don't believe this meeting will take place. Cooler heads seem to have talked with Trump, and he's now saying things must happen before that meeting could happen (and those things are unlikely to happen).
This could be a good thing. A meeting between the two narcissists would be doomed to failure (with North Korea refusing to unilaterally disarm and the U.S. refusing to lift any sanctions). Such a public failure could give Trump the excuse he has been searching for to laugh a military attack on North Korea. He has been wanting to do that, but so far cooler heads have talked him out of it. They might no longer be able to do that if he is embarrassed by a face-to-face negotiating failure.