While hints of it are scattered here and there in The Clone Wars and Rebels, the direct story of the World Between Worlds is told in Season 4 of Rebels, the last season of that show and the first Star Wars project of any kind that Disney released after purchasing Lucasfilm.
Ezra Bridger, a Jedi, lost his master, Kanan Jarrus. Kanan died saving Ezra and other members of the Rebels crew from a huge explosion. But that wouldn't be the last time Ezra heard from Kanan.
Kanan's will (I guess you could say spirit, but I actually wouldn't go quite that far) is carried on through a special wolf creature on the planet Lothal, the same planet we saw in the first episode of Ahsoka, where Ezra is originally from and where Sabine is living when we see her in the Ahsoka premiere.
Before he died, Kanan visited a Jedi temple on the north side of Lothal. There, Kanan learns some incredible truths about ancient Jedi ways, but he never really gets the chance to explain them to Ezra before he dies. But later on, this wolf creature of Kanan's brings Ezra a stone from the temple depicting three people on it. These people are the Father, Daughter, and Son, all of whom we meet during the Artemis story in The Clone Wars. That's a whole other story that delves into the Force and the prophecy about Anakin (I highly recommend watching those episodes). The key things to know from that story arc for Ahsoka is that the Son and the Daughter represent both halves of the Force and balance each other out.
The Son and the Daughter also have another function. And Ezra (along with Sabine) must figure out their other function using the clue on this stone that Kanan's wolf brings to them. Sabine, using her keen eye for art and symbols, figures it out. She learns that the Daughter opens something and the Son closes something.
When Sabine and Ezra test her theory, they realize that the Daughter and Son open and close portals to another realm.
This realm is called the World Between Worlds.
In this realm, voices from Jedi can be heard from all over. These Jedi can be alive, dead, or from the future (after Sabine opens the portal, Ezra reaches the World Between Worlds and can hear lines spoken by Princess Leia during the Original Trilogy; Rebels takes place about five years before those movies). This World Between Worlds realm has many portals that open to various places across space and time.
This has nothing to do with a multiverse or time travel. In Episode III: Revenge of the Sith, Yoda refers to it as The Netherworld, and mentions to Obi-Wan Kenobi that Qui-Gon Jinn spoke to him about it. Yoda even teaches Obi-Wan how commune with Qui-Gon in this Netherworld. It's quite interesting, actually; the World Between Worlds was talked about in live-action Star Wars before they knew what it would become in the animated shows years later.
As Ezra is walking around the World Between Worlds, a portal opens up and reveals Ahsoka fighting Darth Vader. Just before Vader delivers the killing blow to his former apprentice, Ezra reaches through the Portal, grabs Ahsoka, and pulls her into the World Between Worlds. After her initial confusion about what happened, she and Ezra try to figure out what to do next in this realm when, all of a sudden, Emperor Palpatine attacks. He somehow figures out how to see them in the World Between Worlds and tries to capture or kill them. Ahsoka and Ezra escape, of course, but now they both know that they must never allow the Emperor to figure out how to access the World Between Worlds; that would give him too strong an opportunity to destroy many Jedi across space and time with ease, without them even seeing his attack coming.
Flash forward to Ahsoka, and this week's episode ends with Ahsoka seemingly dying after falling off a cliff. We see her awaken in the live-action version of the World Between Worlds (which looks incredible!).
As she stands, she hears someone call to her "Hello, Snips."
Her former Master, Anakin!
Hayden Christensen reprises his role as Anakin, and he greets her. Keep in mind that Ahsoka takes places about five years after the events of Episode VI: Return of the Jedi, so at this point, Darth Vader/Anakin already has died. It seems dead Jedi go to the Netherworld, just as Qui-Gon Jinn did, and now Anakin.
There are many questions we'll need answered in next week's Ahsoka episode. How did Ahsoka get to the World Between Worlds? Did she actually die? It's possible. It's also possible that someone - presumably Anakin - could have pulled her into that realm through a portal in the same way that Ezra saved her from Vader's killing blow.
There's a lot riding on next week's episode. First, the emotional payoff of Anakin and Ahsoka's relationship should be epic. After what the two of them have been through, they will have a lot to say to each other.
An interesting thing to note: when Ahsoka first awakens in the World Between Worlds, Anakin actually says "You're here sooner than expected." What could that possibly mean? Does that mean that she did die? Does it mean Anakin foresaw other things happening to her later in the future?
What I think is going to happen is Anakin is going to help Ahsoka save Ezra Bridger. Ezra will return and likely will be a key figure in stopping Thrawn from resurrecting the Empire (or defeating his Empire again, anyway). Anakin may know that Ezra will need Ahsoka's help. What would be great is seeing Ahsoka pull Ezra through a portal and out of danger in the same way Ezra saved her from Vader's killing blow.
More than that, though, Anakin and Ahsoka need to clear the air between them. They had quite the tumultuous relationship. Ahsoka felt abandoned by Anakin and the Jedi Order after she was framed for huge crimes against the Republic. After learning the truth about Anakin turning into Darth Vader, Ahsoka also carried around a lot of guilt; maybe she felt she could've convinced Anakin not to turn to the dark side before he became Darth Vader. Either way, I'm hoping there will be some heavy conversations in next week's episode.
It's also important to note that Ahsoka may not actually be seeing Anakin. It could be just a dream state (why would Force Ghost Anakin still have a metal arm?). Or, if theories on the Internet are to be believe, it could be either The Son or The Daughter. During The Clone Wars, The Daughter actually sacrificed her life to save Ahsoka, and The Daughter came back in the form of an owl. We've seen this owl during the show; it follows Ahsoka everywhere she goes. There could be some crazy shenanigans going on with this, which would be a huge twist. I feel like they will lose even more fans if they went this route, because a lot of people will have no idea what's going on, even moreso than now; though it would help to have watched Rebels, to this point I don't think not seeing Rebels makes it too hard to follow along with the events of Ahsoka.
The World Between Worlds could open up a can of worms with the rest of the Star Wars universe should Dave Filoni or other writers decide to change Star Wars history in any way. Despite the delicious idea to somehow retconning the Sequel trilogy, I would rather them leave everything alone and just use this time in this realm to set up future Star Wars projects, specifically in this timeframe. Luke is at the height of his powers, and he's building a Jedi Academy. Grogu is around. Han and Leia will have their child, Ben, soon. Hera's son Jacen has Jedi heritage (Jacen's father was Kanan). Add in Ahsoka and Ezra, and suddenly there's quite a force (no pun intended) of Jedi around at this time. Plus, the Mandalorians have a whole other set of stories that can bring them into the fold. All of this could be setting up epic battles against Thrawn and his resurrected Empire (no doubt this is planting seedlings for The First Order along the way). This is the direction I hope they're taking with the franchise.