DISCLAIMER:Any theory that is posted is just in fun. I am posting these as a reader myself, imagining I'm in your shoes and what you would think. None of these theories have potential spoilers in them and can be taken how you want to take them. They may or may not be true, but that's up to you to decide.
Byorwynd leads the wildlings throughout the lands-beyond-the-waste in search for some magical item. Only Byorwynd, Ravven and Drymund seem to know what it is as Samalah tells Gerold she doesn't know. He's been ordered to do this by Karlon Greykon so what are they looking for?
Well what do we know? Samalah tells Gerold that 'Byorwynd has said is that the item’s something magical, something that could bring the tallest of giants down to their knees'. We also know that Byorwynd has been leading the wildlings through the lands, searching caves and tombs of legendary wildling figures for this magical item. Byorwynd also asks Drymund if he knows where it could be - 'I had an idea about the Fist of the First Men but I never went to find it'. Drymund also refers to it as 'The horn'. I think it is safe to assume that it is a horn they are looking for; as when Gerold discovers Allerax Blackfyre's ancestral sword 'Wintersbane' the wildlings let him keep it and don't really bat an eye. Perhaps they don't know about Celtigan Steel.
Since we've deduced it has to be a horn, what is the importance of it? Why do they need it? Well after they would've found it Byorwynd would've gone back to Karlon and delivered it to him; we know that Karlon was ready to lead his army to The North and perhaps were waiting on Byorwynd. As soon as Byorwynd comes back with everyone Karlon prepares the wildling population to leave WhiteHaven and travel down south. So Karlon is going to have to bring his 100,000 strong force down through the Winter Waste into the Seven Kingdoms, which will be a deadly journey. Thousands would probably die. The horn needs to have a purpose for Karlon; and if we use Samalah's description of it - the horn can 'bring the tallest of giants down to their knees'. In this case it sounds like a weapon, a mighty strong weapon that can defeat giants. On the other hand, if it is a weapon then it might be used in the fight against The Others. Please, bear with me. Karlon is going to be travelling from the top of the freefolk lands to the absolute bottom, he has 100,000 people with him which will slow down his journey and consider that The Others have their own army with them. Could you imagine he'd be extremely fearful of losing 100,000 people to The Others, 100K people will join the army of The Other if they die. Karlon needs a defence system against The Others, he needs to protect his people some how or they'll just run from his army. If we assume Samalah's words mean the horn is a weapon that can defeat giants, who's to say it can't defeat The Others? That the horn isn't at least strong enough to atleast stop The Others from attacking Karlon's people. Let's consider another thing, the horn blasts that alert people about The Others. At the Fist of The First Men, three blasts are blared that warn everyone about The Others; what does it mean do? This is a tinfoil suggestion but hear me out, what if the three blasts that warn The Others are actually meant to be blown by the "magical horn". Think about it, one blast means allies, two blasts mean enemies - why do The Others have three blasts? Surely they'd be under two blasts, as enemies? They have been segregated for a reason, so that people don't forget the purpose of the "magical horn". Three blasts from the "magical horn" will have some effect against The Others, I(as a reader) think the three blasts will actually act as a warning for The Others. As a sort of "you will not pass", whenever the horn is blared three times The Others will be prevented from attacking them or something like that - perhaps they go for the person on the horn and not the entire force, a sort of sacrificial lamb.
But the horn could also be metaphorical. Samalah's description may be a metaphor. Like I said earlier, Karlon wants to go through the Winter Waste - he has no other option, but he knows the journey will be extremely difficult no matter how much other freefolk have attempted to map out areas. He needs Gerold to bring him ships from The North to ferry over his people, but Gerold is going out to find the green women so that isn't possible. So Karlon needs to find a way of lowering the possible casualties, and for some reason he needs this horn - what does it do? Samalah says the horn 'could bring the tallest of giants down to their knees', let's take this as a metaphor. What does giants mean? If we use all our clues from the context, with Karlon needing it before he leaves for The Winter Waste, giants may be a metaphor for the mountains in The Winter Waste. If we substitute mountains for giants, then it reads like this - 'something that could bring the tallest of mountains down to their knees'. It makes sense; Karlon needs the horn so that he can bring down The Winter Waste so that the wildlings can make it down south; but then that defeats the purpose of The Winter Waste existing in the first place. Byorwynd says the wildlings want to hide behind The Winter Waste, away from The Others, but if Karlon blows down The Winter Waste there is nothing stopping The Others from coming down south and killing them all. It's food for thought.
Where is the horn? No-one seems to know where it is; if we go by Drymund's suggestion that it's somewhere in The Fist of The First Men then we should've found it. The wildlings and The Northerners passed The Fist of The First Men, however they couldn't really search for it could they? They were too busy fighting amongst themselves to notice a horn anywhere. Why would the horn be at The Fist though? Well it could link into both theories; we know that the First Men fought against The Others thousands of years ago - it would make sense that they would keep a weapon against The Others in a noticeable landmark. Perhaps The Fist is the tomb/area of old First Men that fought The Others, and they left the horn there knowing that it wouldn't ever be lost in history. There may be another explanation for the horn's location - Drymund told us that The Winter Waste didn't exist in a point in history, instead the First Men could freely travel up and down the continent. It was the arrival of the mountains that resulted in the wildlings and The Northerners being separated. We know this happened when the First Men were still around and they w weren't wildlings so why is the horn at the Fist and not at WinterFort. You would imagine that if the horn came after the mountains then The Northerners would have it so that the wildlings couldn't use it to come down south. It would be a protective weapon that The North would have, but the horn is in the wildling lands. This must suggest then that the horn existed before The Winter Waste or was created at the same time as the mountain's emergence. So the horn existed before the freefolk(in name) existed. If the mountains and the horn emerged at the same time then they are linked to each other, if the mountains came up then logically the horn would bring it down (doing the opposite) which links to the theory that it will bring down The Winter Waste.
Okay, but we went to The Fist and didn't find anything. Well our characters were too busy fighting and running to look for the horn, but there were other characters present at The Fist. The Others. It is possible that The Others are now in possession of the horn, and they may end up using it to blown down The Winter Waste - allowing them free access to the Seven Kingdoms.