For Jaime in particular, this was an important moment, seemingly indicating he really had turned away from Cersei once and for all.
Both Cersei and Brienne are referred to as mirror images of Jaime, but while Cersei represents his worst self, Brienne represents his potential, and shows him the honourable man he can be.
Leaving Cersei to help the North – and fight with Brienne – at the end of Season 7 was a crucial turning point for Jaime’s character and his quest to reclaim his honour. Moving forward in his relationship with Brienne, and committing to stay with her in the North, seemingly marked the completion of his seasons-long redemption arc.
Except, of course, this is Game of Thrones, where there’s no such thing as a happily ever after, apparently…