What is the history behind Vikings season 6? I mean what makes the characters in it important, what was going on at the time, and what happens next?
Disclaimer: I've not checked the latest seasons in detail, neither.
In addition to some roughly historically (or, inspired by the later saga traditions) figures illustrated below by /u/sagathain and my cluttered previous comment to this thread, I can say little with certainty for the coming season 6 since the episode had already deviated itself much more freely from kinda 'original' later traditions since seasons 2/3+, as also pointed out by /u/Gankom below.
While the show's timeline across the North-Western Eurasia had already also sporadically deviated from the timeline of the events (most notably in the show's treatment with Rollo) in real Viking Age Europe, the show seems to progress now up to the events VERY roughly corresponding with those occurred in the latest decade or two decades around the year 900.
So, I suppose some events and quasi historical figures from the latest ninth-century and the beginning of the tenth century will be featured in the season 6 with possible very free 'tweaks', as shown by the casting of Prince Oleg [of Novgorod], originally taken from the Russian Primary Chronicle.
The following are just some examples of such additional historical-legendary figures around 900 (no particular order), though I'm not quite sure whether this kind of 'foreseeing' in ongoing historical drama series is tolerable in accordance with the required standard of this subreddit.
(Added): NB: The 'Great Heathen Army' began to dissolve after the death of Ivar the boneless (d. 873) in course of the 870s, and King Aethelstan of Wessex did not take York until 927 (the battle of Brunanburh would occur in 937), so I'm personally not so sure whether the show will progress with the event originally happening in the 930s in this season.
References:
Before we get going, full disclaimer: I've not seen most of the show, I'm looking up summaries of each episode for this, but I know the main plot.
So, to take each part in order:
The main plot of Vikings is taken from two prose narratives: Ragnars saga loðbrókar and þáttr af Ragnarssonum. Both of these follow Ragnarr Lóðbrok, a legendary king of Denmark (NOT Norway, as he is in the show!) and his sons, mainly those with Áslaug Brynhildardóttir. These sons are familiar names from the show: Ívarr, Björn, Hvitserk, and Sigurðr. Additional information and characters are taken from Saxo Grammaticus' Gesta Danorum, the Icelandic Landnámabók (Book of Settlements), the Anglo-Saxon Chronicle, and the East Slavic chronicles
Taking some of the characters in no particular order to talk about them and why they're important:
Ragnarr: Historians are conflicted if he ever existed. Some have proposed that his story conflates the deeds of multiple people raiding in England. However, the saga is a Legendary Saga (fornaldarsaga), so I prefer to read it as entirely fictional. Still, many prominent Icelanders in the Middle Ages traced their ancestry back to him.
Rollo: Rollo of Normandy is a well-attested historical figure. Charles the Simple granted him Duke of Normandy in 911 in exchange for defending the coast against other raids, so Charles could focus on squabbling with his brothers. Rollo and Ragnar were not contemporary! Rollo was born c. 860, after Ragnar would have died.
Lagertha: Lagertha appears in the Gesta Danorum as Ragnar's first wife (Þóra is his second, and Áslaug his third, then). Saxo describes her as a warrior who eventually returns to Norway, marries there, and then murders her husband and becomes queen. This is, to Saxo, a horrible thing; his views on women are problematic to say the least. Lagertha is almost certainly fictional.
Ívarr Boneless: Ivarr (or the old form Yngvar) appears in the Anglo-Saxon Chronicle as one of the exceptionally brutal leaders of the "Great Heathen Army" that conquered Northumbria, Mercia, and East Anglia between 865 and 925. He is described as founding London in Ragnars saga and as founding York in þáttr af ragnarssonum. In the latter, his ghost protects York until William the Conqueror unburied him and burns his corpse in 1066. No record shows him becoming a ruler in Norway.
Alfred: Alfred appears to be one of the main characters for this final season. This is Alfred the Great, who began expanding Wessex and forcing back the Norse armies. He re-took London in 886 CE, when Norse raiders had occupied the town since 875. He is one of the most famous kings of "England" and is still renowned as a scholar and patron of the Church in addition to his military success.
Flóki: Flóki, or Hrafna-Flóki, was the first Norse person to sail to Iceland, though he returned after a bad winter in the north of the country. He also gave the country its name, after seeing the glaciers, probably near Ísafjörður. He, however, did not think it was Ásgarð, that is dramatic license by the show.
Haraldr: this is Haraldr hárfagri, who is listed in most of the sagas as the first King of Norway. He likely did not control much territory in actuality, but he gets credited with unifying the country. Many Icelanders left Norway for Iceland during his reign, many supposed to escape his tyranny.
Oleg of Novgorod: another disputed figure historically, he may have moved the Slavic capital to Kyiv, founding the Rus. He was a powerful ruler, supposedly attacking Constantinople in 907, though Byzantine sources do not record this.
What happens next:
The show deviated from the stories of Ragnar and his sons after season 4, with Ælla's death. This is where both of the sagas end. None of the Ragnarssons are attested going to North Africa or the Rus, so at this point it is largely original material. However, by 925 (thanks, u/y_sengaku for correcting me on those dates!!!), the Norse elite will be forced out of England in Brunnanburh, Haraldr will be the most powerful ruler in Norway, Gorm the Old will be laying the groundwork for unifying Denmark and its Conversion, Oleg will be dead and the conversion of the Rus by Byzantine missionaries will not be far off. The descendants of the Ragnarssons will mostly be in Iceland, where they will become the most powerful families on the island. As to how the show will end, though, the historical material gives few hints.