I LOVE this story, and I think it has some very interesting implications for Bran's situation in ASOIAF. I disagree with PJ about what is happening in the somewhat confusing final scenes; I believe that, as with many GRRM stories, these final pages impart a significant twist on what we thought was going on up until then. So this is what I will focus on here; I agree that the overall recap by PJ was excellent so I won't repeat what was already said.

First, let me point out some important points that led me to my interpretation of the ending:

1. When Holt and his crew emerge from drive, they find out that the laws of physics no longer apply, and this is why their instruments don't work. This is very important: On Grayrest, space and time are not governed by the laws we know.

2.When Holt consults the Damoosh wisdom pool, he keeps asking what is further in. Here is part of their final answer:



There are tales of shipless sailors - but what would these be? How could one get from world to world without a spaceship? [Hint: Holt finds out at the end of the story ]

3. The Stone City consists of a hundred or more separate sections, each with a different architecture and building materials:



It appears that this city was once home to over a hundred different races from a hundred different worlds, each having built a section of it in their own style of architecture. Given that no architecture at all is found elsewhere on the planet, it seems that only this one city was built on Grayrest, to serve as a temporary stop over point for travelers, much like the Dan'lai airfield is today (and also similar to Vaes Dothrak and possibly Asshai - one city in an otherwise empty world, where nobody lives permanently but many travelers pass through, maybe stay a while, and move on. It's a meeting place- a Crossworlds, which is of course the ancient name of this otherwise empty, desolate planet.)
In fact, we see similarities even in the slums of present day Grayrest, where the different alien races have their own sections that they live in. Except the ancient Builders weren't trapped, they used the stone city on the planet Crossworlds as it was intended to be used: to travel from world to world without the need for spaceships. It's no wonder then that the ul-nayileith, upon discovering the city's secrets, began to worship the Builders (despite fearing the stone city and not using the technology).

4. Like many cities on Planetos, most of the stone city is underground. Given the considerable investment in above-ground architecture, it seems the races using the city were not simply tunnel-dwelling creatures but rather lived aboveground. So the tunnels must have served a separate purpose, a shared purpose that was important enough for a hundred advanced races to cooperatively build a meeting place above the tunnel system. (It is likely that one of these races, or perhaps many together, built the tunnels and understood the space/time distortion well enough to engineer the Crossworlds. Then again, maybe a much older race built them, vanished, and the hundred races found the tunnels and were advanced enough to understand their function. They then built the City on top, and used the Crossworlds for trade, exploration and possibly war/conquest as well).

5. Those that go down into the tunnels don't come out. They simply vanish, as those ancient races vanished so long ago.

“Susie Benet isn't here,” Holt said. His voice had a hard edge to it. He began to tick off names on his fingers. “Susie vanished with the Captain. Ditto Carlos. Irai suicided. Ian tried to shoot his way inside the windwalls and wound up on them. Det and Lana and Maje went down beneath, trying to find the Captain, and they vanished too. Davie Tillman sold himself as a Kresh egg host, so he's surely finished by now. Alaina and Takker-Rey are vegetables, useless, and we don't know what went on with the four aboard the Pegasus. That leaves us, Sunderland, you and me.”

This of course makes sense if time passes more slowly down below, as we learn it does later on. They have been waiting for the Captain for a year, but the Captain may have only been down there for a few minutes. I'll get back to this later.

In addition to the time distortion, of course, the tunnels provide entries into different worlds. Those who vanish in the stone city, a million years ago as well as today, don't die down in the tunnels, but enter some other world and don't return (or don't return for so long that they are believed to be gone, when for them, not much time may have passed).

6. Here we get a glimpse of science, to give us a heads-up that space/time is malleable and that with the right technology, it can be warped in such a way as to travel much faster than FTL. It's not as fast as travel using the Crossworlds, of course, but then this drive is only made by the Dan'lai, who are really not all that advanced as alien races go.



So there are different technologies that can be used to distort the space-time continuum. We know this continuum is distorted on Grayrest, and specifically in/by the stone city, as none of the equipment works and the normal rules of physics don't apply there.

7.

The Crossworlds is a transit point, a place where you stop briefly while traveling from one world to the next. The stone city on it is older than time. This may be meant more literally than it is in other contexts; time doesn't follow the same rules in the tunnels below the city; in fact, given the very last paragraph of the story, it may not pass at all. The city may not be affected by "time", it may have been built in such a way that time simply doesn't exist below it.

8. We get our first hint at time distortion (specifically, passing more slowly) in the vicinity of Grayrest as soon as Holt and his crew emerge from drive:



The Dan'lai jump gun is supposed to cut travel time in half - but here, they took 3 months to cover a distance that would normally take six times as long.
Sunderland thinks the jump gun is even better than promised, but why would the Dan'lai undersell their technology by a factor of 3? It seems more likely that by any means, they would have arrived sooner than expected simply b/c as they got closer, time passed more slowly.

9. So now Holt goes down into the tunnels, and here we have our first clear indication of the space-time distortion occurring in the tunnels:





Holt has been going down for a long time, but he is in a window looking down at the city. It is also night, despite Holt having descended the stairs in the morning. Even if he descended for several hours, it should not be night yet. Time moves more slowly underground, compared to its faster passage above.

10.

Another distortion in space. The stone city does not operate by rules that men can understand.

11.

Holt has found the Crossworlds.

12.

Here Holt sees his home world, Ymir, and even his old house. The fact that snow can blow in through the door means it is not just a vision, he could enter the world if he chose (and does so, later, in other worlds).
It is noteworthy that the first door he comes to is the door to his home world; it seems almost as if the Crossworlds takes you where you wish to go, that the destinations are chosen by the traveler. (This is probably the same "technology" that lets the candles in the House of Black and White make each person smell their own happy memories, something that also applies to weirwood paste and shade of the evening.)

11.

This part is confusing. Does Holt really see Sunderland? Why does he disappear/turn into the Shed-boss? The best explanation I can come up with is that this is the Shed-boss testing Holt, to see if he is ready to give up his past life to become a traveler. Once Holt turns away from Sunderland, the Shed-boss reveals himself, and then goes on to "turn on" the various doors and show Holt around:

12.

(...)



There are other travelers using the crossworlds, mostly beings like the Shed-boss but also all sorts of strange aliens that Man has never encountered. Remember that earlier in the story, we were told that the Shed-boss seems to just "appear" suddenly from nowhere - I bet one of the tunnels leads him directly into his Shed.

13.

The doors are not viewscreens, nor do they show visions: they are entryways into different worlds.

14.

Holt comes to the same conclusion I have: people go down into the tunnels and use them to return to their home worlds (or enter other worlds). That (combined with the time distortion) is why they never return.

14.

I'm not sure what's going on with the blind Dan'la, but again, we see evidence that this is not a place where one goes to see visions, but a crossworlds where one can travel from one world to the next simply by walking through a doorway.

15.

Now we know for sure: the doorways take a traveler where he wishes to go- he only has to think it, and the door takes him there. What an amazing technology! No wonder the Builders were worshipped by later races once those races realized what they had built.

16.

Holt intends to go get his friends "in a little bit". But that's not what happens. Kindly, GRRM explains it all to us in the last paragraph:



It's really not confusing at all, is it? The planet is named Crossworlds, and for a reason: it's a place to travel from world to world, and like the shipless sailors of legend, you need no spaceship to do so. In the days of the Builders, the Stone City was used by over a hundred races from far flung worlds, who each built a section aboveground as well. The aboveground part of the city was probably used for trade more than anything; it seems unnecessary for the traveling function of the tunnels, as demonstrated by the fact that Holt continues to travel long after the city has turned to dust.

I will return to this when I have time, and discuss its implications for Westeros, but I will leave you with a final thought:
Despite being a marvel of technology, built and used by incredibly advanced races from many worlds, the Stone City was abandoned and forgotten. When later races, such as the ul-nayileith, discovered its function, they shunned the city out of fear but worshiped the Builders. They knew better than to use the technology.

We know the tunnels can open to any world desired by the traveler, including new worlds he has never been to or even knew existed. This is incredibly useful ... but also incredibly dangerous. (Sword without a hilt...). What if one were to open a door to a world best left alone? What if one alerted a hostile race to the presence of one's world, and could not close the door to keep them out?