In House of the Dragon season 1, episode 10, "The Black Queen," while encouraging aggression towards the usurper, Aegon, Daemon Targaryen takes stock of the dragons on their as well as the enemy's side. Daemon wants the Greens to be prepared for aerial battles as he plots to war. He states that the enemy - the Greens have three dragons by his count (Aemond's Vhagar, Aegon's Sunfyre, and Helaena's Dreamfyre), while the faction he serves - the Blacks have his mount, Caraxes, Rhaenyra's Syrax, Baela's Moondancer, Jacaerys' Vermax, Lucerys' Arrax and Joffrey's Tyraxes. Daemon is bold enough to assume, Meleys is on their side, when in reality her rider, Princess Rhaenys Targaryen is yet to declare for his wife, Rhaenyra.
When Rhaenyra is hesitant, Daemon is eager to plunge the Seven Kingdoms into war. He pays no heed to Rhaenyra's reservations and continues to assess their standing. He tells the council that Seasmoke remains unclaimed on Driftmark, and Vermithor and Silverwing remain riderless on Dragonmont. Daemon mentions three more wild dragons nesting in Dragonstone and says their beasts outnumber the Greens' by thirteen to four. When Rhaenyra questions who are to ride the unclaimed, or wild dragons, Daemon offers no solutions other than his war strategy. His plan sounds simplistic; they host their armies at Harrenhal, cut off the west, surround King’s Landing on their dragons, and trap the Greens. While Rhaenyra's question needs a solution, Prince Jacaerys Velaryon will come up with the idea to employ baseborn dragonriders in House of the Dragon's future.
The First Night
To answer how Jacaerys Velaryon got the idea to search Dragonstone for Dragonseeds, it is important to delve into the Targaryen marriage tradition of the First Night. It is a well-known fact that the Targaryen patriarch, Lord Aenar escaped the Doom after paying heed to his daughter's prophetic dream showing the destruction of Valyria. He moved his household, and dragons to a volcanic island (Dragonstone) off the east coast of Westeros. The Targaryens built a large castle on the island of Dragonstone and a small port which they used as a trading outpost of the Valyrian Freehold. The Targaryens with Valyrian blood in their veins, got stronger with time and eventually rose above the rest and one of them named Aegon Targaryen conquered Westeros.
The tradition of the First Night dates back to the time of the Targaryen migration. The smallfolk of Dragonstone were captivated by their rulers of Valyrian origin, as they had platinum, silver hair and eyes in varying shades of purple, or light blue. To them, the Targaryens were almost on the same level as the gods themselves. With race distinctions embedded deeply in their social structure, a Lord of Dragonstone could invoke his lordly rights of the First Night, which would entitle him to bed a bride on her wedding night. While the bride was considered "blessed," the child, if conceived of such union, was bestowed with lavish gifts by the father. As such, the children who inherited Valyrian features were said to be born of "Dragonseed," and eventually, were known as seeds.
The Wise King, Jaehaerys I's Queen, Alysanne Targaryen overheard many disturbing stories about the First Night marriage tradition. She brought them to the small council's attention who agreed to abolish the practice. While the Seven Kingdoms considered the First Night tradition as vile, some Targaryens continued to practice it with the wives of fishermen and some such. During the Dance, Rhaenyra's eldest, Prince Jacaerys Velaryon suspected Dragonstone was full of Dragonseeds who would have some Targaryen blood in their veins. Such men would be able to claim the riderless and wild dragons and thus be able to serve the Blacks in the Dance.
Dragonseeds In The Dance of The Dragons
While HBO's House of the Dragon brought up the problem of unclaimed dragons, Prince Jacaerys will find a solution to it during the civil war. Realizing the dire need for dragonriders, he makes lavish offers, including knighthood to any man who would be able to master a dragon. Furthermore, Jacaerys announces that the sons of any such man would receive a noble rank and his daughters would be wed to lords. While his lavish offer gains the attention of many men other than Dragonseeds, most candidates fail and lose their lives. That said, some of the notable Dragonseeds include Hugh Hammer who bonded with Vermithor, Ulf the White who bonded with Silverwing, Addam of Hull who tamed Seasmoke, and a woman named Nettles who rode Sheepstealer.
It remains unknown whether these successful candidates had the blood of the dragon, and whether that allowed them to master dragons. Nonetheless, such men (and a woman) are referred to as Dragonseeds for the rest of the Dance. Interestingly, dragonriders namely Ulf, Nettles, Addam Velaryon and Hugh Hammer will fight beside Jacaerys in House of the Dragon's upcoming naval battle fought in the Gullet. While Jacaerys rides Vermax, Ulf the White joins him on Silverwing, Nettles on Sheepstealer, Addam Velaryon on Seasmoke, and Hugh Hammer on Vermithor. As of now, it remains to be seen how the Blacks at Jacaerys' behest will use Dragonseeds to their advantage.