I’d describe those panels more as ‘in medias res’ than a flashback. It’s somewhat difficult to describe what’s going on without getting into spoilers because a) the guy hasn’t been properly introduced yet and b) he’s at the center of a couple major plot twists in the story. Basically, the guy has just told her that he is about to leave her, potentially forever, and she doesn’t want him to leave. Then she remembers that there’s something important she needs to tell him related to why she doesn’t want him to leave.
If you really want more context than that (Warning: MASSIVE SPOILERS INSIDE)
The boy is 鮫吉/Samekichi, Wadanohara’s fourth familiar. At the beginning of the story, he is believed to be a traitor who stole an important artifact protecting the Sea Kingdom from an evil version of the sea called the Sea of Death. In reality, he was loyal to Wadanohara all along and the actual traitor framed him for the crime. Wadanohara and Samekichi were there when the theft occured and knew who the actual traitor was, but the traitor cursed Wadanohara to lose her memories of the theft, and that her mind would get destroyed if she remembered. So Samekichi pretends to be the traitor to drive her away from the sea and keep her from remembering.
The actual traitor eventually reveals themself and opens a gateway that releases Sea of Death, Wadanohara gets her memories back, and everyone realizes Samekichi wasn’t the traitor all along. At the very end of the story, Wadanohara confronts the traitor, but he attacks her and escapes back into the Sea of Death. That’s when Samekichi tells her that to save the Sea Kingdom, he’ll go into the Sea of Death after the traitor and seal the rift from the other side. Which means he’ll be trapped in a hellscape and potentially separated from her forever.
Which leads to the scene in the beginning, but with more context:
Then she has some flashbacks relating to how he promised to protect her from the traitor’s curse (not including those screenshots to limit spoilers) and some more flashbacks relating to the time they’ve spent together in the past:
Which leads to the “more important thing” she’s finally realized she needs to tell him:
But honestly, if you don’t understand exactly what’s going on in that scene, I wouldn’t worry about it too much because you’re not supposed to understand the significance of that page at this point. By the end of the manga it will be a lot more understandable.