With such masterful storytelling as Avatar: The Last Airbender, you can expect even the most minor of background characters to have rich and inventive backstories. The beloved series was often effective at communicating as much of those stories as possible, but when it came to Fire Sage Shyu there was just too much to fit into his debut. The history of the Fire Sage is fascinating and may make Shyu one of Avatar's most interesting minor characters.
The only episode that Shyu appeared in, "Winter Solstice, Part 2: Avatar Roku" had quite a lot going on, so it's no wonder that only so much of Shyu's story made it into the episode itself. After learning that he needed to commune with his predecessor Roku through the former Avatar's statue at the Fire Sage's temple on Crescent Island. While most of the Fire Sages were loyal to the Fire Lord and sought the Avatar's capture, Shyu was the sole exception and helped Aang and his friends complete their mission.
During the episode, Shyu mentions that the conflict between his family and the Fire Nation's royal family began with Sozin, but the conflict and Shyu's backstory only really get fleshed out in additional content like the Avatar Extras event and lore provided by the Nickelodeon website. While most fans may never be aware of it, learning the story of Shyu makes the "Winter Solstice" episode even interesting.
Shyu's story really starts two generations earlier with his grandfather Kaja, who was also a Fire Sage. As the spiritual leaders of the Fire Nation, it was the Fire Sage's role to serve the Avatar, the Bridge Between Worlds, and in that capacity, Kaja became Roku's firebending master. As fans are well aware, however, everything changed when the Fire Nation attacked. While most of the nation believed the Avatar was slain with the genocide of the Air Nomads, it was Kaja who was the first to speak out in his belief that the Avatar survived.
But Fire Lord Sozin demanded loyalty from the Fire Sages, boldly breaking with the tradition of generations. Kaja passed his convictions on to his son and the boy grew up to become a Fire Sage as well but was executed for his beliefs, making Shyu the third in a generation of Fire Sages bravely trying to maintain a spiritual tradition in the face of their order and entire country blindly following monarchical demands. When Shyu saw the signal of the Avatar's return upon Aang awaking at the South Pole, he knew it was up to him to do whatever he could to aid the Avatar and restore balance to the world.
That all serves as the backstory for Shyu leading up to everything the audience sees in "Winter Solstice," giving the episode an emotional story of legacy that makes such a small character into something far grander. Going beyond the series, Shyu's story even continues in the comic Smoke & Shadow, where it turns out he holds a position of honor under Zuko as the Great Sage at the High Temple in the Fire Nation Capital City. His imprisonment under Ozai's regime now a distant memory, Shyu loyally serves the new Fire Lord and frequently offers meditation classes Zuko politely declines.
Various bits of lore from the Kyoshi novels to Smoke & Shadow to other content delves into the importance of the Fire Sages, with their origins even intertwined with that of the very first Fire Lord upon the unity of the Fire islands that form the eastern archipelago. So much of the lore is not commonly accessed content to most fans, and yet Shyu stands out as the tip of the iceberg right there in an episode from the original series' first season.