Stanza 3 Summary

Get out the microscope, because we’re going through this poem line-by-line.

And this was the reason that, long ago,
In this kingdom by the sea,
A wind blew out of a cloud, chilling
My beautiful Annabel Lee;

Here's where things really take a turn for the worse. The speaker blames the terrible turn of events on the angels who coveted him and Annabel.
The jealousy of the angels was the reason why a wind came down from a cloud and killed his girlfriend.
Actually the speaker doesn't tell us right away that she dies, just that the wind was "chilling" to her. That's a great word to use because it makes us think of the way you get sick in bad weather (like how people say you "catch cold").
At the same time, it gives us a first creepy hint of Annabel's cold, chilled dead body, which is a major theme for this poem.

So that her highborn kinsman came
And bore her away from me,
To shut her up in a sepulchre
In this kingdom by the sea.

Then, still without saying that she was dead, the speaker tells us how her "kinsman" (that just means a member of her family) came and took her away from him.
Be sure to notice the word he uses to describe this kinsman. He calls him "highborn" which means aristocratic, noble. If the speaker himself were "highborn" he probably wouldn't think to mention this. Since he does, it gives us a little hint of a conflict here, maybe a little bit of a Romeo and Juliet-style family feud.
Maybe even before she died there were problems in his relationship with Annabel Lee. That's just a small example of how Poe can work neat details into what seems like a simple story.
Whatever is going on with the family, you can feel the speaker's pain at losing Annabel, and you can tell that he feels she is being stolen from him.
He tells us how the family "bore" (that just means "carried") her away from him.
Death and Annabel's family are trying to tear these two lovers apart, to "shut her up" in a "sepulchre." (That's another word for a big fancy building that you bury someone in, a tomb like you might see in an old cemetery. It's also a perfect Poe word – you can always count on him to go for a spooky, fancy word when he can.)