The joke is a metaphor.

In that scene, the Batman has asked the Joker how can he help him, maybe together they can find a way to really cure the Joker; this reminds him a joke, that goes along this line:

See, there were these two guys in a lunatic asylum... And one night, one night they decide they don't like living in an asylum any more. They decide they're going to escape! So, like, they get up onto the roof, and there, just across this narrow gap, they see the rooftops of the town, stretching away in the moon light... stretching away to freedom. Now, the first guy, he jumps right across with no problem. But his friend, his friend did not dare make the leap. Y'see... Y'see, he's afraid of falling. So then, the first guy has an idea... He says 'Hey! I have my flashlight with me! I'll shine it across the gap between the buildings. You can walk along the beam and join me!' B-but the second guy just shakes his head. He suh-says... He says 'Wh-what do you think I am? Crazy? You'd turn it off when I was half way across!

Batman has somehow dealt with his bad day (the death of his parents), the Joker hasn't: he went crazy.

You could say Batman has jumped out of the asylum roof on the other palace (sanity), while the Joker is the scared guy: he is really scared to deal with his misery, to deal with his bad day and with what he has done after that day, he will never jump; the Joker thinks that Batman's offer of help is foolish like telling a guy to walk on a light beam; he is too scared and cannot be saved anymore.

I am convinced that in the end:

Batman kills the Joker

since he has understood that this is the only way to help him out of his misery (that's why Batman laughs: he understands how foolish he was).

What was the conclusion of that scene or what was the actual meaning of that? I couldn't understand the ending of the movie.

It's intentionally left up the audience to figure out what it means. It is lifted straight out of the source material, the 1988 comic The Killing Joke by Alan Moore and Brian Bolland. So much so that 20 years later, Bolland explains the ending in the afterword for the 2008 re-release:

Speaking of which, it’s time I revealed what really happened at the end of The Killing Joke: as our protagonists stood there in the rain laughing at the final joke, the police lights reflecting in the pools of filthy water underfoot, the Batman’s hand reached out and...

He doubles down on the ambiguous ending. The other half, Moore, has never outright explained it. The ending is debatable as to why Batman laughs, if he snapped, if the Joker really gave up, if Batman killed him or not.

But As ComicAlliance explains it, and I agree:

[M]ost important, is what Gordon says to Batman about bringing the Joker in by the book. This represents the entire point of the story. The Joker is trying to prove to everyone — and himself — how close they are to being just like him. And despite everything he does to Gordon — crippling his daughter, torturing him — he’s okay, and he’s still determined to show the Joker that the system, with all it’s flaws, is inherently sound, and that the Joker is wrong. He knows he’s wrong, and Batman needs him to be wrong.

It also follows what Batman has been saying this entire time, that he has to try to save Joker, give him the chance, which is why he goes to Arkham in the beginning of the film.

That said, there's always the other interpretation. Batman is trying to stop the Joker from killing himself. Like he did the other most influential Batman comic, Frank Miller's The Dark Knight Returns just 2 years earlier, which was also turned into an animated film, 2 (okay 3) years earlier.

They just laugh together

Since relevant, I'll refer to the comic, on which the movie's based. Both other answers are on track.

Context for several views on this story

• It's commonly regarded, as by cde, to be an open end: it's claimed to be what the script shows.
• There's even material to say, as by mattiav27, that Batman kills the Joker, and this is what Grant Morrison believes. Cool explanation here is that GM notes that both characters begin to laugh and then one of the laughs stops, and the light shuts out, so the bridge goes away. In fact in the comic story you can see that they both begin to laugh and in one of the last vignettes both laughs appear syncronized and later on one laughter just ends. But even if one would to accept this murder angle: how do you know who kills who? According to Morrison Batman chokes the Joker... But:

the art alone appears to debunk that reading just based on where Batman places his hand, which comes to rest on The Joker’s shoulder rather than wrap around his throat as Morrison states. Moreover, the script doesn’t indicate anything as far as Batman strangling The Joker goes. (Though in fairness, there’s a lot that can happen off the page between writer and artist.)

An interesting theory, though hardly new: as noted by Bleeding Cool, Bolland himself [the illustrator of the comic] referenced the idea of Batman killing The Joker – which has been discussed among fans since its release – in his afterword for the recolored edition of The Killing Joke in 2008.

• Perhaps even both Batman and Joker dying, both poisoned: "But was that ambiguity really intended? The script, so verbose about intention, leaves that aspect out." "There’s another solution of course. That the death of the Joker is there, intentionally, but it’s not from Moore [writer]. It’s from Bolland [illustrator]."

• One theory maintains that the first and last panels of the book are both purposely of rain falling on the ground, which symbolizes that nothing has changed: "The ending was purposely left uncertain to allow the reader to decide what happened".

• Yet another note on the background light that dissapears: it may mean that the boundaries that distinguish Batman from The Joker have disappeared.

Explanation and answer of why they just laugh together

The author-writer of the comic, Alan Moore, gives his almost official version of the story, after explaining that he's not a big fan of this piece of work of his, he states:

for the record, my intention at the end of that book was to have the two characters simply experiencing a brief moment of lucidity in their ongoing very weird and probably fatal relationship with each other, reaching a moment where they both perceive the hell that they are in, and can only laugh at their preposterous situation. A similar chuckle is shared by the doomed couple at the end of the remarkable Jim Thompson’s original novel, The Getaway.

Futher on, in this last page script vignette #3 illustrates the idea that the whole crazy situation is just a joke: they may as well enjoy this one rare moment of contact while it lasts.

Since most people are saying that the ending conclusion is up to the audience to decide i feel like its the end its done now the reason for batman laughing well that's tough knowing that his sense of humor isn't like anyone else's just like the jokers so they both share and have a lot of things in common but mostly the whole abyss thing how they accepted it joker isn't afraid he just accepted his personal abyss as the batman they probably dint share the same type of abyss but they have accepted it so if the joker and joker realizing that when batman tells him what Gordon told him about "doing it by the book" he realizes they are crazy for "doing it by the book" and the batman realizes joker will never be sane again which is why i think he laughs what else can he do??..I don't know if this made sense too anyone or if you kinda got my point understanding of the ending on Batman "The Killing Joke"....LilB951 June 16, 2020 1:48 a.m