If we know anything about George R.R. Martin, it's that he loves to set up enticing mysteries in the Game of Thrones books and then go several thousand pages without ever mentioning them again. The Sunset Sea is one such mystery. We know that it lies to the west of Westeros, and that no one has ever been able to cross it. We know that there are stories of ancient men (or perhaps ancient sea creatures) coming from the distant west to do weird things like building a cool chair in the middle of the Iron Islands. But that's about it. We don't know what lies across that sea in Martin's exhaustively detailed imaginary world. We don't even know if those far western lands will ever enter into the plot of A Song of Ice and Fire (Martin certainly has enough loose ends to tie up without traipsing off on another sea voyage for several dozen chapters).
So here's everything we do know about what lies beyond the Sunset Sea, and why is just might make it into the series after all.
Firstly, it seems highly likely that Martin's planet is round, like our own, even if it is full of dragons and whatnot. Secondly, Martin hasn't exactly been subtle about the fact that his Westeros is essentially Fantasy England, and Essos is Fantasy Eurasia. Does that mean that the Fantasy Americas lie to the far west, across the sea?
That's possible, but I think it's highly unlikely that Martin's story will ever take us to the Fantasy Americas—he has enough plot to deal with as it is, and plenty of vague, distant lands labelled on the map already.
Another possibility is that Martin himself hasn't decided what's across the Sunset Sea, and all of the weird, vague hints he's dropped are just for added mystery. That might be the case... but Martin does love to come up with backstory, even if he doesn't end up using all of it.
The Iron Islanders who live on the far off Lonely Light, the western-most island in all of Westeros, seem to believe that there are rich lands beyond the Sunset Sea, but that no one has successfully found them yet. Some even believe that Iron Islands were originally peopled by travelers from across the sea, who built the Seastone Chair long, long ago. We'll come back to that.
We also know that one of the Brandon Starks from way back sailed into the sunset in search of lands to the west and never returned. It's entirely possible that he just died at sea, but Starks are notorious for disappearing/dying only to return with a vengeance.
And then there's Dany's prophecy.
Daenerys Tagaryen picks up a new prophecy about herself just about every dang day. One of the earliest ones she receives, though, is from the masked woman Quaithe, suggesting that Dany should travel to Asshai in the far east:
"To go north, you must go south. To reach the west, you must go east. To go forward you must go back, and to touch the light you must pass beneath the shadow."
Asshai, Dany thought. She would have me go to Asshai. "Will the Asshai'i give me an army?" she demanded. "Will there be gold for me in Asshai? Will there be ships? What is there in Asshai that I will not find in Qarth?"
"Truth," said the woman in the mask. And bowing, she faded back into the crowd.
Asshai is the furthest east that anyone in Westeros has ever even heard of. Melisandre hails from a Asshai, a shadowy city made from black stone, where the people are creepy as heck and do lots of sinister magic.
TV Dany is already messing about back in Westeros, but book Dany is still in the east. It's still possible that she will visit Asshai. And it's even possible that she will go so far east that she'll wind up in Westeros, crossing the Sunset Sea on her way to circumnavigate the globe.
And that brings us back to the weird chair in the Iron Islands: It is made of a mysterious black stone, much like the stone that makes up Asshai. In fact, weird black stone makes up the base of the Citadel in Westeros, too, and an abandoned city in Sothoryos (Fantasy Africa), and the Five Forts in the far east of Essos. The weird, ancient black stone exists in places to the far west and the far east of the known world. It's almost as though whoever built all those weird stone things came from the Sunset Sea and ventured out in both directions.
It's almost as though the White Walkers come from there, too.
In the ancient days of Martin's Fantasy Earth, you see, there was a winter that lasted for a generation, filled with demons and darkness (A.K.A White Walkers and their zombie friends). The "demons" came from the north in Westeros, hence why the Wall was built. They came from the northeast in Essos, hence why the Five Forts were built. Both cultures tell the story of a hero, sometimes called Azor Ahai, who eventually rose up to defeat the demons and end the eternal winter with the help of his Very Awesome sword, Lightbringer.
So... could the far northeast of eastern Essos and the far northwest of western Westeros be connected somehow? Or if not, what lies in between them, in the coldest corner of the Sunset Sea? Is that where all these demons are hanging out when they're off duty? Is that the "truth" that Dany is meant to find by continuing her journey east instead of west? Is that the key to getting the seasons back on track and fixing the Westerosi government? Maybe.
Or, you know... maybe it's just a whole lot of water.
We'll just have to wait and see.