I've noticed that a lot of people didn't really get Shadowlands lore, whether because they took a break or just didn't care much for it, so I thought it would be a good idea to write out a short summary for it, just to get you up to speed before Dragonflight comes out
Minor spoilers for the Sylvanas novel!
Three important things before Shadowlands' plot happens:
1. Sylvanas killed herself somewhere around the time Deathwing came out of Deepholm, so the very start of the Cataclysm. Here she met The Jailer who promised her that they can break the cycle of life and death together. They both see it as unfair. He was the first Arbiter and saw countless people's lives judged by the rules set in place by the First Ones, that don't take context into consideration and often split families apart of eternity - he wasn't really down with that, which is why after him, a mechanical Arbiter was put in place. A mechanical Arbiter wouldn't get any smart ideas. After Jailer's servants show Sylvanas how families are separated for all eternity, something she cannot handle as family has been everything for her all her life, she is convinced too. She lost her parents and brother in the Second War and the thought of being sent to the Shadowlands where she cannot see them ever even though they are out there broke her. She is also mortified that the Arbiter sent her to the Maw for doing bad things she was forced to do by Arthas, while sending people like Zul'jin who is responsible for the deaths of her family members and countless more, by his own volition no less, to Revendreth where he can get penance. She decides to side with the Jailer, after deliberating it for years though - right around Legion when she became a Warchief.
2. The Dreadlords are created by Sire Denathrius, the leader of Revendreth who is sided with Zovaal... maybe. As you know Dreadlords are very cunning and known for being deceitful so who knows if Denathrius *really* serves the Jailer, but that's a topic for another time. What is important is that Denathrius sent the Dreadlords to all the different cosmological forces as spies, most notably, Disorder. If a creature consumes too much of a type of magic, it will become a being of that type of magic. So the Dreadlords who consumed Fel became literal demons. There was also a void sect of Dreadlords who manipulated Sargeras into starting his great Burning Crusade. They showed him the soul of the world Argus, which is a Titan. They told him that if Argus' soul was infused with Death magic, it could ressurect Sargeras' demons from the Twisting Nether much more quickly than it would have taken them otherwise. This is very important later. The Dreadlords also gave Kil'jaeden the Helm of Domination and Frostmourne which he used to imprison Ner'zhul at the end of Warcraft II Beyond the Dark Portal, but it was made by the Runecarver in Shadowlands, who later turns out to be the imprisoned Primus. It was supposed to be used as a tool for the vessel who would start the Jailer's conquest on Azeroth, but it's made quite clear that all of them (Ner'zhul, Arthas, Bolvar) were acting mostly to their own accord, besides Arthas who was often manipulated by Ner'zhul.
3. Now you remember that I said that Argus was infused with Death magic. Well, when we killed him in Legion, that broke the Arbiter because a being such as Argus was not meant for the Shadowlands (the Titans who are beings of Order have their own realm of existence) but being infused with Death he became a creature of Death, and the breaking of the Arbiter caused all souls to be sent the Maw instead of their rightful afterlife. This empowered the Jailer and Sylvanas a looot.
So, to empower the Jailer (and herself), the Jailer instructed Sylvanas to cause as much death as possible, thus the Fourth War began after Legion which is central to most of the plot of BfA. After BfA, she goes up to the Icecrown Citadel, fights Bolvar, and breaks the Helm of Domination. The Helm of Domintion is tied to the Shadowlands and every time you break an artifact of power, that power goes back to where it came from. A surge of energy burst from the Helm after it was destroyed and it literally broke the barrier between Azeroth and Shadowlands.
Now what you need to know about are the Sigils of Shadowlands. There are five of them - one for each of the covenants + one for the Arbiter. You need them all to open a way to a place called Zereth Mortis. Zereth Mortis is a literal "Cornerstone of Death", the place where the First Ones made the whole of Shadowlands. At the very heart of it lies the Sepulcher of the First Ones, which is kind of a nexus point between all six Zereth realms (one for each cosmic power). The Jailer wanted to use the Sepulcher to establish his own rules of reality. He also needed the soul of Azeroth, which is a world-soul with a lot of potential to be used as fuel for something like that. But first, the Sigils.
As he couldn't personally get the Sigils himself without going on a huge offensive, he needed pure souls that he could send to each of the realms that would gather the Sigils in surgical precision assaults. To this end, he told Sylvanas that she should choosy worthy people of Azeorth. She chose Baine Bloodhoof, Anduin Wrynn, Jaine Proudmoore, Thrall and Tyrande Whisperwind. All of them got set free in the intro for the Maw, except Anduin. All the stuff in 9.0 happens - covenant campaigns and the attack on Castle Nathria where Prince Renethal binds Denathrius inside Remornia (Denathrius' sword), hoping to give him penance as all souls in Revendreth get. During 9.0 Sylvanas tried to convince Anduin to join them as she saw her brother in him. However when all else failed, Anduin was completely dominated by the Jailer using Domination Magic, which is a twisted form of the Language of the First Ones. It was made by the Primus as a means to imprison Zovaal when he wanted to reshape Reality back when he was just the Arbiter. He also got a sweet new weapon called Kingsmourne that was made with the soul of Arthas. This is where 9.1 happens.
Anduin goes on to Elysian Hold and gets the Sigil of Kyrestia. Sylvanas launches an assault on Ardenweald and gets the Sigil from there, Denathrius gave his Sigil to the Jailer at some point before Shadowlands, and we find the Sigil of the Primus, an investigation that leads us to Torghast where it is revealed that the Runecarver is the Primus. Since we have the Sigil with us, Zovaal takes it from us pretty easily. Now all that was left was the Sigil in Oribos.
But before that, some semblance of order is brought tot he Shadowlands. The Kyrian change their philosophy of wiping memories, the Maldraxxi finally have some order after the whole civil war, Revendreth is much more stable and in Ardenweald we finally get an answer as to why Elune let the Teldrassil burning happen - she sensed the drought in Ardenweald and let the burning happen because she thought the souls of the kaldorei there would help her sister - The Winter Queen, and Ardenweald. It is also revealed that Elune is a member of the Pantheon of Life. Tyrande also lets go and is cleansed from the Night Warrior's power that could have easily killed her eventually.
Another big thing that happens is that the Dreadlords take Remornia, which still has Sire Denathrius bound inside, and take him... someplace. We still don't know where he is or what he plans to do, but it's safe to assume he will come back with a vengeance.
Before the Jailer tries to strike Oribos, the covenants unite and launch an assault at the very heart of Torghast - the Sanctum of Domination. We get to the very top of Torghast and fight Sylvanas, but before we can beat her, the Jailer sends out chains to Oribos. We chase after them on these chains, eventually ending up in the Arbiter section of Oribos, where we actually lose and the Jailer manages to obtain the last Sigil and also gets a sweet new armor. He spouts about how everyone will serve him. Sylvanas bowed to never serve anyone after the shit she went through with Arthas, and Jailer assured her before that they are partners, equal. So she sends an arrow at him in protest. Obviously it wasn't gonna do anything, it was a sign of protest. The Jailer then tells her that it's a pity, but he did help her get something that was his (the Arbiter's Sigil, he used to be the first Arbiter), so he gives her back the part of her soul that Frostmourne took and leaves for Zereth Mortis.
We manage to slowly reforge the five sigils and go to Zereth Mortis where we chase after him and Anduin. We manage to free Anduin, beat the Jailer using the reforged Helm of Domination - now called the Crown of Wills that is able to resist the Jailer's Domination magic which is like 80% of why he's so powerful, and we also make a new Arbiter - Pelagos from Bastion. He vowes to never send souls to the Maw ever again. Then comes the judgement of Sylvanas. Instead of judging her himself, he lets Tyrande do it. She sends her to the Maw where she will have to free every single soul that was ever sent there, back to the Arbiter, where he will judge them. Sylvanas jumps into the Maw and that's that.
In 9.2.5 we get some nice epilogue stories - Undercity is cleansed of the Blight and a new leadership is put in place consisting of figures high in the Forsaken society. Calia Menethil is also brought into the fold, while kaldorei Dark Rangers are allowed to return to the Alliance if they so wish. Anduin visits Sylvanas in the Maw where they talk for a bit and we find out that Anduin feels intense guilt over everything the did while Dominated. And lastly, the Winter Queen gives Tyrande a seed empowered by saved kaldorei souls that can be used to plant a new World Tree.
Regarding what might come next, there seems to be a confirmation of a Seventh power existing and that it stands in opposition to the six ones we know of. In essence, it could just be two cosmic forces and the six could just be aspects of the first one, while the second one stands in opposition. That's it for the story of Shadowlands, hope this cleared some stuff up.
This post is also available in video form if you prefer to listen -
https://www.youtube.com/watch?v=WFGMZhVlynA
If you have any questions feel free to ask