The Fire Sages are the religious authority of the Fire Nation, responsible for identifying the Avatar's incarnations when he is born in the Fire Nation, guarding the temple and conducting weddings and funerals for the Royal Family and to those who seek their help.
There is probably a connection between the earliest Fire Sages and the Sun Warriors, as Zuko notices that Sun Warrior buildings are architecturally similar to the Fire Sages' temples.
Long ago, in its earliest years, the Fire Nation was ruled by the ancestors of the current Fire Sages. A council of Sages led the Nation with a strong sense of spirituality held to the highest degree, much similar to the spiritual Air Nomads. However, the Sages have since lost their power to the Fire Lord lineage and currently direct their energy on serving merely as council to their ruler. They used to be completely loyal to the Avatar and the Avatar alone.
They are seen at Roku and Sozin's birthday party announcing the identity of the then next Avatar (Roku). After Avatar Roku died, Fire Lord Sozin started the war. The Fire Lord set forth a decree that anyone who helps the Avatar will be considered a traitor to the Fire Nation and dealt with appropriately. The Fire Sages then switched their allegiance to the Fire Lord. When Aang entered the Avatar State in The Southern Air Temple all the avatar temples around the world were notified, including the Fire Temple. Now the last of their kind, the modern day sages are little more than aging remnants of a time where spirituality was placed before military might.
The Fire Sages learned and inform Fire Lord Ozai of the Avatar's return in "The Southern Air Temple", when Aang's triggering of his Avatar State causes various statues and murals within Avatar Temples around the world to become supernaturally illuminated. Later in "Winter Solstice Part 2: Avatar Roku", the Five Fire Sages confront Aang and his friends and attempt to prevent him from speaking with Avatar Roku, chasing the three around the entire temple. One sage, Shyu, betrays his associates and helps the three trick the remaining Sages into opening the doors of the sanctuary that holds Roku's statue. Once inside, Aang meets with Avatar Roku and together, the two combine to destroy the temple, allowing Aang and company to escape in the process. In the end, the Five Fire Sages are blamed by Admiral Zhao for the upsetting failure and all are arrested.
Their next appearance was when they were about to coronate Azula as the next Fire Lord, when Zuko and Katara arrived. Instead of finishing the coronation, they watched as Azula and Zuko fought, although this was because Azula challenged Zuko to an Agni Kai for the crown. They were last seen in the final episode where they conducted Zuko's coronation as Fire Lord.
The Fire Sages have another Fire Temple located in the Fire Nation Capital, the Fire Sages Capital Temple. Below this building, are the Dragonbone Catacombs; it keeps the history of the Fire Nation and its Fire Lords within the catacombs.