The job to the North that Goblin Slayer takes is to act as an ambassador of sorts, in the sense of introducing the concept of Adventurers to a patch of northern territory that has been recently annexed into the Kingdom.
Their role is to show their faces for the purpose of introducing Adventurers... and to scout out what life is like in this distant land, which was only known in tales and legends for many in the Kingdom.
This quest, according to things revealed later in the book, is supposed to be Gold Adventurer stuff, but the King chose to extend the offer to Team Goblin Slayer after some endorsements from Sword Maiden and his own Sister (though the latter was masked as being from the Earth Mother Church, of course).
Of course, given what the series is, their endorsements work fine, with Team Goblin Slayer managing to show their value the Northmen; so much so that they promise to extend their thanks to all other Adventurers who pass into their realm by the end of the volume.
Well, helping the Northmen hack apart what seems like a younger brother of Cthulhu while taking apart yet another group of Goblins (though the Northmen were handling the Goblins just fine until said Horror From The Sea popped up and massively screwed things up) certainly helped in that, along with Priestess charming the whole group by being her usual self back at their town.
The people of this land call themselves "Vikings" (yes, very original, ha ha, though the reading is slightly tweaked to keep with the Not!Norse theme), and worship a set of gods slightly different from those in the south. Such as a flipped version of the Earth Mother, to which Priestess initially twitches about since that one is known in the south as a Goddess of Torture, but in the harsh, cold north, she is seen as a warm figure who knows the harshness of what life is in the north and yet extends a warming embrace.
(The eyepatch woman, who is called "Fuss-Freiya" (フースフレイヤ in the JP), is a Priestess of said Goddess, by the way, and her mark on her eye and arm is from getting struck by a bolt of lightning in the eye when she was a child. She had taken this as a divine sign, which lead her to taking the path of becoming a Priestess, or "Kija" in the tongue of the Northmen, of said Goddess, and it lights up when casting miracles from said Goddess, as depicted at the end of the volume.)
Their relationship with the different races is interesting too; the Elves are seen as rare and a source of semi-worship, while the Dwarves are known to have steady trade with them, and the Lizardmen are basically unknown.
(The funny part is that the Northmen start treating HEA and Lizard Priest as being together, if simply because they accidentally (or not, it's kept vague on HEA's part, while Lizard Priest is oblivious) do something only married couples do amongst the Northmen during a party. And then a good chunk of the text seemingly starts to ship them together in a sense......)
The ruler of the patch of land claimed by the Kingdom is actually the King's uncle by marriage, due to the previous King taking the man's elder sister as his wife when his family was cast away from the North, and were basically brothers.
The young ruler apparently was sent to the North as a part of a supporting force during the last Demon Lord's rampage, and ended up getting married to the Fuss-Freiya (and it seems to be that said title points to being his wife more than anything) and became the Go-ji, a title as the leader of the Northmen.
Their marriage is depicted to be from love, and that it was basically love from first sight.
The Northmen have their own language, but still not too far from the Hume Common that most of the characters use in the series, with the Go-ji being the only one to speak fluent Hume Common since he grew up in that environment.
Even then, the Fuss-Freiya is depicted as trying to learn the Common, simply because her husband insists at taking her to the Kingdom's capital and she didn't want embarrass her husband; her husband, on the other hand, is depicted as being furious as how some of those in capital easily dismiss his wife as a "bear of a woman" which he sees as being rude and unfair.
Since, from the Priestess's point of view, the only other woman who could stand up to be compared to the Fuss-Freiya in terms of beauty is the Sword Maiden, this makes sense.
On the other hand, the Northmen are depicted as having customs that are pretty barbarous to the south-folk, like mutual raids being a fact of life and that some cases of marriage happen in the shape of kidnapping the wife-to-be during such a raid, although it is considered to be good taste to go through the proper motions for marriage if you are not in a tight spot.
(The Northmen section basically kicks off with Team Goblin Slayer witnessing such a raid in the town they were travelling to, and getting told that raids being this frequent (as in, nearby settlements being that close to going hungry) was never heard of. A 'prisoner', who was basically left behind as a messenger, tells of the troubles of the nearby settlements.)
While going over the Misty Mountains (I call it that since the chapter that deals with said mountains is named "Over The Misty Mountains") that divide the Northmen from rest of the Kingdom, Team Goblin Slayer stumbles upon a Dwarven Fortress (which gets referred to as a "Dwarf Fortress", which is obviously a shout out) which has been long abandoned and taken over by Goblins. They fight through the Fortress, and in the process, Goblin Slayer picks up a very sturdy Dwarven Blade, which he ends up taking home as a trophy, even asking the Northmen to make a scabbard for it.
(The volume has Goblin Slayer starting to cherish certain weapons for their value, like never throwing a sword given to him from the Northmen for the final battle of the volume and handing it back stating that it is too good a blade for a person like him to use afterwards. Of course, his friends notice this change.)
Oh, and did I state that Priestess is depicted at hearing Goblin Slayer laughing, something he hasn't done since Volume Six, by the end of their adventure in the North? Yeah, he does that while asking a Northman his 'pay'; a scabbard for the Dwarven Blade he picked up, and a promise to treat Adventurers with the same respect that Team Goblin Slayer were being given by that point.
...On the topic of Shipping, I'm guessing that the GS and Cow Girl couple is basically a foregone conclusion, though Guild Girl is trying to cover the gap.
Heck, it gets depicted that unlike the others, Cow Girl could tell how absolutely giddy GS is while showing her the stuff he brought home and trying to tell her about his experiences up north (which is spoken in his typical way so she has to coax it out of him, but still) at the end of his section of the story.
The end of the volume depicts the newbie from Volume 13, the "Roguelike" PC who has the name of @, stumbling into the Northmen, and introducing herself as an Adventurer.