Disclaimer: Spoilers ahead for the third episode of Game of Thrones, Season 8.
When you play the Game of Thrones, you either win or die... and you watch the Game of Thrones you know that no dialogue, scene, or song is as simple as it appears. Like in the latest episode, Jenny's song that Podrick Payne sang. (Also, who knew even singing was one of his many talents that the ladies loved!).
The song is one of the many from books that made it to the series (yay readers!), though Podrick's version has more lyrics - and possibly a greater significance.
When the song plays, the camera pans over the major characters, most of whom are with the ones they love, like Arya and Gendry, Grey Worm and Missandei, Sam and Gilly, and of course, the Tormund-Brienne-Jaimie trio. The song also plays in the background as Jon shares the truth about his ancestry with Dan.
This could hint at what the upcoming Battle of Winterfell entails for the characters and their loved ones. (Of course, there are going to be deaths and tears).
However, per the books, the song was sung by the ghost of a prophetic woods witch High Heart about her friend Jenny of Oldstones, who had a doomed affair with Prince Duncan Targaryen.
As per the books, Duncan Targaryen was the brother of King Aegon V's and Mad King Aerys' uncle. However, per the show, he was actually the original heir to the Iron Throne and Aerys' brother. Since the show creators have always tried to simplify the family lines, a change in the Targaryen family line is actually not unexpected.
Even though the song, with limited lyrics, is referenced in A Storm of Swords, the actual story behind the song is revealed by the wise Knight Barristan Selmy, in the book A Dance with Dragons. He shares the story with Daenerys.
The Prince of Dragonflies loved Jenny of Oldstones so much he cast aside a crown, and Westeros paid the price in corpses.
Essentially, the Prince was convinced of his love for Jenny to the extent that he abdicated his crown and broke off his planned engagement to the daughter of Lord Lyonel Baratheon. That's when Aerys aka The Mad King took over the throne.
There are two more inferences that the song hints at, one from the past and one from the present.
In the past, it is assumed that the song also refers to the forbidden love affair of Rhaegar (Daenerys' brother and Jon's father) and Lyanna Stark. In the present, the song could hint at a Targaryen forced to choose between duty and love - which frankly, seems to refer to Aegon aka Jon more than Dany at the moment.
If the legends and past experiences are to be believed, then it does appear that Jon may choose love over duty. But will that lead in love lost or a battle won is something that is impossible to predict!