In 1953, North and South Korea agreed to a truce and the establishment of the 38th Parallel and the DMZ. There was no formal end of hostilities, so yes, the Korean War has been ongoing for the past 65 years, even though there has been no fighting. One thing the two leaders agreed on was to formally end the war.
As to why this is happening?
I've seen speculation that NK's nuclear test site is either in extreme danger of collapsing, or has already partially collapsed, perhaps making the site unusable, or unusable without the danger of total collapse and a dangerous nuclear fallout on par with Chernobyl. Now, while I doubt Kim Jong-Un gives much of a damn about his peasants getting irradiated to death, he probably A. cares about HIM getting irradiated to death, and B. China getting irradiated to death, as the fallout from that would undoubtedly threaten large swaths of China, something the Chinese government would take a very dim view of indeed.
There's also the speculation that the north has just run out of nuclear material. They can't make bombs anymore, they can't test bombs anymore so there's no reason to be a douche about it anymore.
There's also the sanctions perhaps having an affect on the country and the threat of starving peons actually rising up is getting to a point of danger, and the army's loyalty might not be as strong as the government would like.
Then there's China which, while a staunch ally of the North for the past 65 years, has started to sour on the North as Un waves his nukes around in the US and the South's faces. China doesn't want a nuclear war on their doorstep as the fallout would undoubtedly affect China's territory.
Lastly, there's also the fact that Trump is sort of crazy and might just make good on his threats to end the North's nuclear ambitions on his own terms. And with Kim Jong-Un's track record of threatening the US at every other turn, the rest of the world might just see Trump as justified were he to attack.
Do I think anything will come of it? Well, I could probably throw Kim Jong-un farther than I trust him (and I couldn't throw that tub of lard very far without the help of say a trebuchet), but I remain cautiously optimistic. I won't be surprised if nothing comes of it, but I imagine I'll be pleasantly surprised of something good does happen.