The Dark Souls franchise is all about cycles. Civilizations come to power and they spread and grow, only to overextend, and be reduced to nothing but dust. The same goes for the Undead curse that drives men mad. These cycles continue over and over and it seems like there's never anything anyone can do but restart it with a head start.
Anor Londo being in Dark Souls 3 seems to be a product of these cycles. Not only do ideas come back up after a time, but so does architecture and technology. In Dark Souls 3, Anor Londo bears a striking resemblance to its predecessor but also sports some changes of its own.

No More Sun

A close look at the architecture of Anor londo in Dark souls 3
In Dark Souls 1, Anor Londo starts off as a shining beacon of hope for society. It's depicted as the center of culture and the embodiment of power since it acts as a capital to the empire of Lordran. As the player progresses through the city, it becomes clear that all is not what it seems and that King Gwyn has cast an illusion over his people.
If the player kills his son Gwyndolin, the illusion subsides and the bright sun disappears into the sky, revealing a dark void. The people of Anor Londo were fooled by their king, and the illusion is nowhere to be seen in Dark Souls 3.

Irithyll Theories

Player overlooks Irithyll in Dark Souls 3
In Dark Souls 1, the player can look down from Anor Londo and see a city below. The city is just assumed to be a part of Anor Londo, and not much care is given to it. Since the release of Dark Souls 3, players have started to wonder if the city below was always Irithyll? The city was cast into an endless night of cold and dark before anyone can remember, and is located directly by Anor Londo.
The theory would suggest that when Gwyndolin died, the false sun disappeared from the sky and darkness fell over the people. That would explain why the city is so advanced but also so cold. They have everything they could need from paved roads to extensive sewage systems, and yet nobody can actually inhabit the city due to the darkmoon and the scourge.

Ornstein And Smough

The iconic duo in dark Souls 1
Ornstein and Smough were legendary warriors who served the empire well in Dark Souls 1. They're also a fan favorite boss fight because of their unique mechanics and extreme difficulty. When players first saw the gates of Anor Londo and the layout from the first game, they began to wonder if they would experience the iconic boss fight again.
Unfortunately, neither makes an appearance in Anor Londo as a fight, but Ornstein's armor has made multiple appearances. In Dark Souls 2, players fight the Old Dragonslayer who wears the armor that resembles a scaled dragon. The armor also gets possessed in Lothric Castle in the Dragonslayer fight in Dark Souls 3. Smough doesn't get the same treatment though, which is strange since Ornstein was able to appear in all major installments of the series.

Giant Blacksmith

The dead giant blacksmith in dark souls 3
In Dark Souls 1, players have to infiltrate the main gates of the castle in Anor Londo, and make their way up a pathway to the left at the top of the stairs to find the Giant Blacksmith. He's a giant of few words who's capable of infusing weapons with upgrades other blacksmiths can't. He also keeps great arrows in stock which are useful in certain situations. The Blacksmith quickly became a fan favorite with his catchphrase "shiny, shiny".
In Dark Souls 3, he's still in the exact same place, but the door is unlocked, which is curious. Upon further inspection, players find that he has long passed on and has dropped a Giant's Coal, his own little shiny item. Nobody knows how he passed or when, but it's interesting that his body remained behind. How old was the giant to survive countless cycles between Dark Souls 1 and 3? How old was he in Dark Souls 1? These are questions fans will probably never get solid answers to.

No Longer In Lordran

Dark Souls 1 Anor Londo before the sun illusion is dissipated
One big and obvious change is that Anor Londo's location has completely changed from where it was in Dark Souls 1. The original kingdom of Lordran is no more, and Anor Londo has moved into a new kingdom. It's hard to say how this happened, but whenever a new cycle begins, and the flame is lit again, worlds collide and rearrange themselves on top of one another.
Anor Londo could simply be a relic of a past empire that existed even long before the events of Dark Souls 1. This would explain why its appearance hasn't changed at all in Dark Souls 3, and why the same enemies are there, accompanied by new ones.

Silver Knights

Silver Knight of Dark Souls overlooking Anor Londo
In Dark Souls 1, silver knights roamed the halls and roads of Anor Londo looking to defend it from invaders who could pose a threat to Gwyndolin. The knights were armed with spears and swords and shields, generally common equipment for knights in the game. Between the 1st and 3rd game, they made a few changes.
When the Knights are confronted at the steps leading to Anor Londo, they actually have weapons imbued with lightning. Lightning is seen as holy in the Dark Souls universe as it was used to smite dragons and build the empires of the world. It's interesting to see the knights grow in power and gain universal lightning on their weapons, as if the empires didn't stop trying to expand even though they were in "times of peace".

Yorshka, The Half-Dragon

The half breed of Dark souls 3 and captain of darkmoon blades
Yorshka is a half-dragon bred being who sits atop a tower, isolated from the main towers of Anor Londo. She sits there gazing off into the distance, waiting for a time when she can leave and return to her people. Yorshka wasn't a character in Dark Souls 1, but she's very reminiscent of someone in the series who came before her.
In the original Dark Souls, players could enter the painted world from inside a painting in Anor Londo. After completing the painted world, players met Priscilla, another young girl who was half-dragon in blood. Both girls seem young and wistful, and are locked away in towers away from humanity, to hide their true nature.

Dark Moon Knights

A darkmoon Knight in Dark Souls 3
After players find Yorshka, she gives a speech after they swear loyalty to the Darkmoon Knight covenant. She claims that she will grant the player purpose, and champion the single knight. Fans noticed this speech sounded familiar and found that Gwyndolin says the exact same thing in Dark Souls 1.
This could mean a number of things, but fans generally speculate that he taught her what he knew when passing down the role of captain of the knights. The absence of the false sun, Gwyndolin's passing, and Anor Londo are all tied together in the identity of the abandoned city, as well as the Darkmoon Knights. The progression from the first Dark Souls to the last is a great metaphor for the futility of linking the flame and how eventually, the warmth will die out, just like the knights.

Influence Of The Deep

In the Anor Londo keep, there's an abundance of evidence of just how far the darkness has spread into the castle and city nearby. For starters, just above the center of the main entrance, there's a Deep Accursed clinging to the ceiling waiting to pounce on unsuspecting victims. Obviously, the deep didn't exist in Dark Souls 1 so this is a new addition to the Keep.
On top of the monsters roaming the halls, Aldrich's cursed flesh is also all around the keep, adding to the eery and dark atmosphere. What once was a symbol of wealth and power in Dark Souls 1, has turned into a place of darkness and sickness that spread to the people who were gullible enough to follow it.

Overall Layout

The titular bonfire of Anor londo in Dark Souls 3
Out of all the callbacks in Dark Souls 3 to older levels, bosses, and weapons, the inclusion of Anor Londo is one of the most noticeable. There're so few differences between the new Anor Londo and the old one that it feels like an abridged version of the same level. The biggest changes made in Anor Londo are the areas around the castle itself.
Players can now explore a courtyard, underneath the Great Keep, and a path that leads to a new tower, which are all completely new areas. Exploring new areas in a familiar place is something fans of the series can appreciate, especially since Anor Londo is one of the most iconic locations from the first game.