Essentially after the tournament and a bit of a time skip, human world and demon world are currently in co-existence. However a certain cult isn't liking this arrangement and demands that spirit world put up the barrier between worlds again. But at their refusal, the cult became a terrorist group taking over the spirit world control center threatening to destroy human world if they don't comply.
So Yusuke decides this will be his last case with his friends as they fight their way through. However upon making their way to the weapon they already rigged it to fire to which Yusuke tells everyone to evacuate as he disarms it choosing between three buttons which can do one of three things being fire on human world, self-destruct destroying him in the process, or disarm it (blue button). As it concludes to that beach scene you see in the anime, Kuwabara explains to Keiko the reason why Yusuke chose the blue button saying in quote 'if those cult guys have their god then I have my goddess' which Yusuke refers to Keiko as blue is her favorite color.
As it goes along, we learn of what happens to each of them. Kuwbara and Kurama just goes to live normal lives of college students.
Yusuke opens a ramen stand which also doubles as a supernatural detective agency to which his business seems to be doing fine.
Yusuke's biological father is revealed (finally).
Hiei kind of hooks up with Mukuro as he gets revenge for her by torturing the man that tortured her in her youth.
Finally for Koenma, he succeeds his father as king of spirit world when he was caught trying to brainwash some demons into causing trouble in human world giving reason to put the barrier back up. With Koenma as king, he removes the bounty spirit world put on Yusuke's head.
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