The episode title refers to the advice Maester Aemon gives Jon about growing into a man of the Night's Watch, how he must mature into it and make selfless decisions. This is the same advice he gave many years ago to his own brother Aegon V Targaryen when he was crowned king: "Kill the boy, and let the man be born." As is often the case with Game of Thrones episodes, the title may carry a double meaning: it may also refer to the story that Roose Bolton tells his son Ramsey about how he raped Ramsey's mother, and was presented months later with an illegitimate son; Roose was briefly tempted to kill the boy, but reconsidered.
When Tyrion blacks out after being pulled underwater by a Stone Man (filmed in a swimming pool in Belfast), it's the longest blackout ever in Game of Thrones history. They wanted people to momentarily think he had died. The blurriness you can see as he regains consciousness was achieved by cinematographer Greg Middleton holding his fingers over the camera lens.
The way Sansa's hair is worn during the dinner scene with Ramsay and Roose is almost identical to how Catelyn wore hers.
Maester Aemon's age is not explicitly stated in the show. According to the books he is 102 years old and believed to be the oldest living person in Westeros. The Three-Eyed Raven is 125 years old in the books, but most believe him to be long dead.
This is the first time that Old Valyria, the ancestral land of the Targaryens, appears on the show. It was destroyed and shattered into many tiny islands during the Doom of Valyria, a series of volcanic explosions known as the Forteen Fires. The ruins on the show are visually inspired by the ruins of Angkor Wat, a largely submerged and overgrown ancient Buddhist temple in Cambodia. In the books, there is mention of the "Red Skies of Valyria", an ominous red glow in the skies which may come from active volcanoes, or something unknown. On the show, when Drogon flies over, the glow is indeed there, in reference to the books, although it comes from the sunset.