The original Dark Souls had two endings. If you look at the game from a long distance, with only a rudimentary understanding of the lore, it looks like one is the "good" ending and one is the "bad" one. In the seemingly good one, you Link the Fire. As we find out in the third game (maybe the second, though aside from Demon Souls this is the entry in the series I know the least about,) Linking the Fire has actually become a tradition.
Gwyn, who was basically the King of the Gods, was the first to link the fire, sacrificing himself to burn for ages within the Kiln of the First Flame to prevent it from burning out. The first Dark Souls takes place during an era that you could sort of think of as a second near-apocalypse. There was the earliest Age of Dragons, where things were in a gray stasis, and then the Age of Fire, and then this kind of second Age of Fire after Gwyn sacrificed himself. But with the time bought by that sacrifice running out, you, the player, have the option to Link the Fire and extend the Age of Fire into a third epoch, though it will mean you spend the rest of your existence burning and losing your mind as you go Hollow - not from a lack of purpose, but because whatever you have that can burn (likely your Humanity, though I don't know what exactly Gwyn had to burn) will eventually run out.
What we see in DSIII is that the player character, if they choose this ending, becomes the first (or really second, as we should probably count Gwyn) Lord of Cinder - the name given to individuals (or groups, in at least one case) who link the fire at the end of their epochs and extend the Age of Fire.
The "bad" or more specifically "evil" ending, at least if you look at it without much nuance, is the one in which you abandon the fire. In this case, you allow the fire to fade and walk out into an Age of Dark.
Dark of course has mostly negative connotations in most culture (we're not really nocturnal animals, at least we weren't until electric light made it easier to be) but in Dark Souls it's far more complicated than that.
Darkness is associated with the Abyss, a corruption that seems to spread through the world and turn people into monsters and places into nightmares, but it's also the thing that defines Humanity. Of the four Lord Souls discovered at the beginning of the Age of Fire, the Dark Soul was the one that was found by the Furtive Pygmy, who was either the creator or the literal father of humanity.
As I understand it, the Humanity sprites that we use in DSI are all fragments of this Dark Soul, which the Pygmy gave to his people. Absent humanity, humans would revert to mindless Hollows, which means that the Dark Soul seems to be necessary for humans to have minds and thoughts.
So is an Age of Dark one that is fated to see the spread of the nightmarish Abyss? Or is it one in which humans will gain better self-awareness and power to forge their own destinies? Or both?
There's a kind of sneaky question that pops up in the first Dark Souls game. Gwyn and his fellow Lords rose to power in order to bring about an age of disparity and change. They rebelled against the Everlasting Dragons, who had been happy with the cold stasis of their Age. But Gwyn's efforts have been to prolong his own Age.
In the period of Dark Souls 1, this doesn't seem that unreasonable. Lordran is certainly in a state of ruin and decay, but the world itself doesn't seem totally unhealthy. Refreshing the world and bringing things back to a state of order (closer to what Anor Londo is like) seems like a pretty good idea.
But in Dark Souls III, it's less obvious that the world is worth saving. Pretty much every place in the world is in decay - not just the urban centers of civilization, but also the countryside. Perhaps some of this can be blamed on Prince Lothric's decision not to Link the Fire and the ensuing delay in this renewal, but there's also the possibility that the Fire is just not in a state to be renewed. It's like the difference between giving a 20-year-old a kidney transplant versus a 90-year-old. That young adult will make great use of it and probably be back to normal in a short amount of time, but even with a life-saving surgery, the old person is still not expected to bounce back to their physical prime (apologies to any 90-year-olds who are reading this.)
As Unkindled Ash, it's your job to get the reluctant Lords of Cinder or would-be Lords of Cinder (in the case of Lothric) to do the duties they abandoned, namely to once again Link the Fire. Linking the Fire is in a sense a renewal of the world at the cost of a grand sacrifice (I think we can assume that all the Lords were important people in their day - the Undead Legion of Farron was like a global superpower and Aldritch was almost like an anti-messiah,) preserving the Age but ending the epoch.
So in a sense, it's about sacrificing the familiar world to preserve the world in one form or another, and you could thus make the argument that refusing to Link the Fire is kind of an act of cowardice, preserving your epoch at the cost of the Age.
But maybe that's BS?
After all, this cycle of renewal is actually a cycle of stasis. And we can, under some interpretations, consider this ritual of stasis to be the cause of very unhealthy stagnation. Linking the Fire seems on the surface to be good, partially because it entails something that we in both Western and Eastern societies consider virtuous - an act of self-sacrifice.
But this act also seems to be interrupting a natural order that could, in fact, lead to something preferable.
One thing I wonder about is whether the Refuse to Link ending at the end of Dark Souls 1 is equally canon with the Link the Fire ending. If we abandon the Kiln, does this truly begin an Age of Dark? Does the First Flame die? And if it does, does that mean that the Flames that have been linked by the other Lords of Cinder from Dark Souls III are not actually the same that Gwyn originally discovered? The fact that the Soul of Cinder appears to contain Gwyn as well as previous player characters (not to mention the persistence of some characters like Andre of Astora) make it hard to believe that there's been a totally transformative Age of Dark.
And maybe that simultaneously means that the rebellious act of refusing to Link the Fire as well as the noble sacrifice of doing so are both kind of meaningless. The world does, it seems, always have the ability to bounce back and return to the Age of Fire.
I'm inclined to think that the most interesting ending to Dark Souls III is the "Usurp the Fire" ending, which is the most complicated to achieve and also the most apparently transformative.
Here, we neither allow the flame to burn out nor do we simply preserve the status quo. But if the white appearance of the Sun/Darksign is important (I'd guess yes) then it implies that the fire has truly turned into something different.
What does this new age really look like? We become the "Lord of Hollows," bearing the "True face of man," but that face is, it seems, a Hollow, undead one like how we look with Hollowing (so default) in Dark Souls 1. This is an embrace of the Curse of Undeath. So does this ending imply that the entire world will just be filled with the Undead, but that they will all serve the Lord of Hollows, this kwisatz haderach of the Sable Church? And as hollows, will they be mindless? Or, by taking the flame, does the Lord of Hollows basically grant all the benefits of being Undead while preventing the mindlessness of the Hollow state?
In Ashes of Ariandel, we get a microcosm of all these problems, with a lot of similar imagery. The Painted World, which was meant as an escape from the main world, has been painted over and over, never really getting rid of the old world (interestingly, we see Priscilla's little tower in a valley when it was once high up in the world of Ariamis, not unlike how Anor Londo, which was the highest point in Lordran, is now sunk into the Boreal Valley.) The world is meant to burn, lest it give way to rot, and right now the creator of that world, Ariandel, has been convinced by Elfriede to prevent the burn and preserve that world, despite the rot. Just as in the "real" world, you represent this potential to take part in a cycle of sacrifice and renewal, also involving fire.
But which is really the act of rebellion here? Should the Painted World be subjected to this endless cycle of burning and renewal, or would that lead to a kind of stagnation? Is refusing to participate in the cycle (like Lothric does) actually the truly brave act?
Consider the fact that Elfriede is one of the founders of the Sable Church, which intends to create something new in the "real" world by transforming the fire-linking cycle. What exactly does she have planned for the Painted World? Do we interrupt her before we can discover her true motives?