Tate and Vivien's babies are demonic/satanic (see video preview). The Latin sentence on the piece of paper that the new pope opens in the preview video translates to "A child born from a spirit and a human will usher in the end of times".
We learn about Ben's childhood & backstory. We learn how his relationship with Hayden began, what was going on with Vivien at the time, and why he cheated. 
P.S. (Post scriptum or rather post show in our case): While we did not see Ben's childhood, Ryan Murphy said that we would see it in episode 9. So don't blame us. It's possible, that he once again used the crew's numbering of the episodes, not ours, so then we will see it in episode 10.
The dentist Dr Curan murdered the Black Dahlia. 
Constance discovers more of Tate's bad behavior.
This episode will deal with why the house and its occupants have baby mania.
We will find out why Tate committed the school shooting. The reason is connected to his and Addy's upbringing. "The episode will show Tate's life before his death with Constance and Addy," according to Evan Peters.
Note: It is possible that while Peters said this will be featured in episode 9, this will actually be featured in episode 10. The cast do not count the Pilot as an episode, thus counting differently. Both Denis O' Hare and Ryan Murphy have made this mistake in the past.
Peters says the future, while complicated, is still looking good for Tate and Violet. “There are [still] a lot of secrets between them and all of them come out in the upcoming episode. There’s a pretty big secret that Tate has been keeping from Violet.”
Constance's other son, Beau, will be featured in this episode as well. 
Hayden's older sister, Marla, will visit the house.
According to Kate Mara, there will be a flashback involving Hayden and Ben where you discover how their affair happened, see what their chemistry was like, and what got Ben into trouble. 
Hayden is going to plan/help Tate get to spend the rest of his "life" with Violet. Should she still be alive, this could possibly mean killing her. 
You find out more information about the pregnancy and the twins, and it's not as simple as it seems.
Hayden will see the young Moira doing a seductive dance for Ben.
Kate Mara - "In [next week's] "Black Dahlia" episode, [there's a moment] with young Moira (Alexandra Breckenridge) that shows that we clearly don't like each other and are just living in the same place because we have to." 
Ben learns a harrowing fact about Vivien's pregnancy.