Perhaps I just have a bias against parallel dimensions (as evidenced from my interpretation of Silent Hill's otherworld), but I want to take some time to clear up what might be a mis-conception in the conventional wisdom interpretation behind Dark Souls' multiplayer summoning mechanics. Dark Souls co-op is not necessarily based on parallel dimensions, as many players seem to assume. It might, in fact, be intended to be an abstraction of some kind of time travel. I've noticed that many players online already seem to refer to the multiplayer mechanic of these games in terms of time travel, but I've yet to see any wikis, lore videos, or blogs that seem to explain multiplayer as a time travel mechanic.

I want to preface this analysis by stating that I'm not asserting that the following explanation is the absolute, 100% correct interpretation of the mechanic. Individual players may disagree based on their own reading of the game, and I'm personally somewhat conflicted on the topic myself. I merely want to propose this as a possible alternative to the defacto "parallel worlds" interpretation. I'm going to point out in-game evidence that supports the idea that Dark Souls' multiplayer is based on time travel, but there is also in-game evidence and mechanical evidence that flat-out contradicts that interpretation. I will address those contradictions as well. So that being said, please keep an open mind, and enjoy the read!

The summoning mechanic

There are two games in the series that are not part of the Dark Souls franchise, and which have different in-game explanations and rules for the same multiplayer features (more or less). Those games are, of course, Demon's Souls and Bloodborne. Both have asynchronous multiplayer and summoning mechanics that work similarly to Dark Souls.

Demon's Souls summoning operates under the idea of summoning the spirit of a fellow adventurer who's soul is trapped in the Nexus. This is why you must be in soul form in order to be summoned. Bloodborne's beckoning operates [similarly] under the principle of manifesting hunters out of dreams (which seems to operate under a similar cyclical paradigm to Dark Souls, but I'm not 100% sure). In Dark Souls, you aren't necessarily summoning ghosts (as you do in Demon's Souls), since the undead in Dark Souls are more akin to zombies than ghosts. Also, characters in Dark Souls can leave summon signs whether they are hollowed (dead) or in human form (revived), which is a significant alteration from Demon's Souls. A lore reason for summoning is provided in Dark Souls:

Solaire explains to us how summoning works:
"We are amidst strange beings, in a strange land.
The flow of time itself is convoluted; with heroes centuries old phasing in and out.
The very fabric wavers, and relations shift and obscure.
There's no telling how much longer your world and mine will remain in contact.
But, use this, to summon one another as spirits, cross the gaps between worlds, and engage in jolly co-operation!"

Both Solaire's dialogue, and the White Sign Soapstone (along with other online play items) make references to other "worlds", which leads to many jumping to the conclusion that each player's game is a sort of parallel universe within the Dark Souls lore. However, this may not necessarily be correct. Both Solaire's dialogue and the soapstone also provide explanations for these worlds: "time is convoluted | distorted". This seems to be the explanation for what is meant by "worlds", and it seems that Solaire and the in-game descriptions may be using "time" and "world" interchangeably (could it be a translation / localization issue?). The phrasing in the white soapstone's description joins "the flow of time is distorted", and "the White Soapstone allows undead to assist one another", into a single, compound sentence, which definitely implies that the two phrases (and ideas) are linked.

"Online play item. Leave summon sign.

Be summoned to another world as a phantom through your sign, and defeat the area boss to acquire humanity.

In Lordran, the flow of time is distorted, and the White Sign Soapstone allows Undead to assist one another"

 

The dialogue of Saulden (the Crestfallen Warrior of Dark Souls II) is even more explicit...

Even though the player character in Dark Souls can be in a "hollow" state, the player never truly goes hollow. At least, not in the sense that NPCs and enemies have gone hollow.

According to Dark Souls' mythology, the undead are condemned to repeatedly wander Lordran in search of a cure, being unable to permanently die. But for virtually all such undead, this quest is futile. An undead can temporarily stave off hallowing by absorbing souls or infusing themselves with the humanity of someone else. Eventually, an undead dies one too many times, or is worn down by the daily grind of collecting souls, and loses the will to go on -- or is simply unable to continue collecting souls and humanity. When this happens, that undead becomes hollow, loses his sanity and free will, and continues to wander the world as a mindless zombie attacking any un-hollowed that it encounters on sight.

It is unknown how many "Chosen Undead" are brought to Lordran or the Undead Asyulm, but the Crestfallen Warrior at Firelink tells us that many have come before you. Is it possible that all hollows in Lordran were at some point "Chosen Undead", tasked by Frampt to retrieve the Lordvessel and re-kindle the dying flame?

Probably not.

A great deal of the hollows that you encounter in the game were likely former residents of Lordran, and there was no need to select a "Chosen Undead" until Gwyn's power faded to a "cinder", and the fire began to die. This presumably took a very long time - a whole "age".

The Crestfallen Warrior informs us that we are not the first "chosen undead",
and suspects that we won't be the last either.

Avoiding hollowness with purpose

Many undead adventurers wandered into Lordran (or were abducted and taken there), and they struggle to hold onto their precious humanity for as long as possible, fighting for their lives in the fear that they, too will go hollow. Some, like the Crestfallen Warrior, resign themselves to the inevitability of hollowness, and find a sense of purpose in warning other new arrivals that they, too, are doomed. Others pursue some seemingly impossible goal or objective in the hopes that the journey will provide them with the sense of purpose necessary to avoid (or at least delay) hollowing. And yet others have taken up crafts or vocations such as blacksmithing, vending, or guarding something in order to keep them focused and avoid hollowing (and to exchange goods or services for the very souls that they need to stave off the hollowing). Keeping such a goal may help keep an undead partially lucid, but they also seem to begin to forget everything else, and only the knowledge of their quest or craft remains. Perhaps, the undead guarding various areas of the game were, at one point, tasked with protecting that place (or something within that place), but have long since lost their mind, and only that compulsion to defend has remained.

Going on "one final quest" seems to provide adventurers with enough focus to hold back hollowing.

But hollowing isn't just a thematic element reserved for non-player characters; hollowing is also a mechanic in the game that affects the player. Whenever the player character dies, you are reborn at the last bonfire in a hollowed state, unable to summon help from allies until you restore your humanity through the consumption of someone else's humanity. In Dark Souls II, hollowing further handicaps the player by cummulatively reducing your total health each time you die, and only restoring your humanity can refill your health meter. In both these cases, the player is not truly hollow; you are only in a state of partial hollowing.

It's unclear whether non-player characters are able to die and restore their humanity, or if deaths contribute to an irreversible progression towards hollowness. There are, after all, apparently hollowed NPCs such as the undead merchant in the Undead Burg and blacksmith Lenigrast in Majula who are sane enough to have kept their shops open. The presence of NPC summon signs hints at the possibility that they, too, are capable of restoring their own humanity through the same mechanisms that you can, but the game itself justifies this with ambiguous appeals to "time distortion" and hypothetical parallel realities that obfuscates the matter - particularly where Solaire and Lautrec are concerned.

Summoned NPCs may recover humanity as you do, or they're from another time or dimension, or both.

Solaire's dialogue refers to "heroes centuries old phasing in and out.". Solaire may be using the words "world" and "time" interchangeably. This seems to be the game's justification for how summoning works: you may be literally summoning someone from a bygone era into your own time period. Anytime, you are summoned to someone else's world, you are also being transported to another time (past or future, depending on whether or not you finish the game). Solaire and Lautrec seem to somehow come from another time or dimension, but other characters definitely seem to exist within your world and time: Andre, the Crestfallen Warrior, Rhea and her companions, Big Hat Logan and his apprentice, and so on are all undead who have seen many other "Chosen Undead" come to Lordran seeking their destiny.

In any case, it's not until an undead "gives up" that the hollowing process becomes complete. What do we mean by "giving up"? For an NPC, it means that they gave up on life and went hollow, and the player typically ends up putting them down. For the player, it means that you stop playing the game. As long as you continue to play the game, then your character will continue to hold onto a sliver of humanity and maintain his or her sanity for a little while longer. When you put down your controller for the last time, you have condemned your character avatar to finally succumbing to hollowness, whether you recognize it or not...