Disclaimer: Eu ainda não vi esse episódio do programa, mas, em geral, o programa é incrivelmente fiel aos livros, então eu vou dar uma resposta do livro.

A gravidez de Melisandre é o resultado da magia que ela (supostamente) extrai de seu deus, R'hllor.

Aviso: Spoilers à frente:

The shadowy figure is a magical assassin. It is implied in the books that she draws the energy to create it from Stannis through sexual intercourse.

Não me lembro de mencionar um filho dos livros, mas duvido que seja isso que Melisandre estava se referindo.

Sombra

A Wikipédia do Game of Thrones simplesmente se refere a ela como Sombra . Em uma entrevista com Carice Van Houten (Melisandre) e Liam Cunningham (Davos) Carice refere-se a ele como um "Bebê Sombra".

Can you single out your weirdest or most challening scene?
Carice: Giving birth to the shadow baby would be the answer for both of us. We were there together.
Liam: Yeah, I had a few pains… I felt your pain, darlin’.
_{SEASON 4 INTERVIEW: CARICE VAN HOUTEN & LIAM CUNNINGHAM}

If your character meets an ending like Ned Stark… what memory would you best remember from your time on Game of Thrones?
Carice: The shadow baby! But mostly just being around Stephen [Dillane] and Liam. They couldn’t be more different as actors, and as people. You could see a sitcom about these two guys. It’s a very funny threesome, I would say.
_ibid

Bryan Cogman, um dos escritores do programa, também se referiu a ele como um "Monstro das Sombras".

When was it decided that they were finally going to appear? Well, you had a stand-in for Selyse in the opening of S2, and I think Melisandre makes a passing reference to her, but this is quite a bump up in visibility.
“It was an evolving thing. Season 2, as ever, we had to be judicious about how many characters to introduce. It was decided that, dramatically, it made sense for the S2 Stannis scenes to involve this triangle of characters, if you will—Davos on one side, Melisandre on the other, Stannis being pulled between the two. In the book, you have Selyse on the Mel side but we decided to pull her out of the political discussion, at least for now. But when the decision was made to dramatize the conception of the shadow monster…”
_{SEASON 3 INTERVIEW: BRYAN COGMAN}

Davos parece se referir ao monstro como "Sombra" ou "um horror" em seus capítulos de POV dos livros também.

He could not behold the fiery heart without thinking of the shadow Melisandre had birthed in the gloom beneath Storm's End.
_{A Clash of Kings, Davos III}

"The Mother. She blessed me with seven sons, and yet I let them burn her. She spoke to me. We called the fire, she said. We called the shadows too. I rowed Melisandre into the bowels of Storm's End and watched her birth a horror." He saw it still in his nightmares, the gaunt black hands pushing against her thighs as it wriggled free of her swollen womb. "She killed Cressen and Lord Renly and a brave man named Cortnay Penrose, and she killed my sons as well. Now it is time someone killed her."
_{A Storm of Swords, Davos II}