I see a darkness in you... We WILL meet again. ~Melisandre to Arya Stark in Game of Thrones season 3
Adam Rifkin stashed this in @maisie_williams
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In the books there's a key foreshadowing scene where Arya and the BWB meet the Ghost of High Heart to ask about her visions of the future. Mel's show meeting and the line you linked are meant to somewhat replace that. The book comment to Arya is:
I see you. I see you, wolf child. Blood child. I thought it was the lord who smelled of death ... You are cruel to come to my hill, cruel. I gorged on grief at Summerhall, I need none of yours. Begone from here, dark heart. Begone!
The point of that is that the Ghost of High Heart has many visions of the past and future. She's no stranger to death, and was not bothered by Lord Beric Dondarrion who's personally died and resurrected multiple times. What does bother her was coming in contact with Arya and seeing more death than she can handle. It's more death than the Summerhall great fire catastrophe that destroyed the whole castle and claimed the lives of most of the people there at the time, including the King, two princes, and the Lord Commander of the Kingsguard. It's one of the foreshadowing/prophetic lines that suggest Arya will personally be involved in the deaths of many, many people.
The show doesn't have the backstory to make that as clear, but Mel's comment to Arya is along the same lines.
"I see a darkness in you. And in that darkness eyes staring back at me. Brown eyes, blue eyes, green eyes... Eyes you'll shut forever. We will meet again."