The Age of Burning Fields is a time period of 100 years mentioned in The Legend of Zelda: Breath of the Wild. It had occurred after the fall of Hyrule during the Great Calamity and the seal of Calamity Ganon in Hyrule Castle by Princess Zelda. During this period, the surviving peoples of Hyrule recovered and settlements like Hateno Village where rebuilt.
Anticipating the Great Calamity
One hundred years before the events of Breath of the Wild, King Rhoam Bosphoramus Hyrule and Princess Zelda formed the Champions (Princess Mipha, Revali, Daruk and Urbosa) to use the excavated Divine Beasts to combat the return of Calamity Ganon who had been defeated using the ancient Sheikah technology ten thousand years earlier, initiating the 10000 Years of Peace.
Fall of Hyrule
After Link was defeated by the army of possessed Guardians and the demise of the Champions at the hands of Ganon's minions, Zelda entrusted the Master Sword to the protection of the Great Deku Tree and returned to Hyrule Castle and used her power to seal both herself and Calamity Ganon within it, bringing about a brief period of peace for the surviving people of Hyrule.
Age of Burning Fields
The sealing of the Hero
After these events, Impa, Dr. Purah and Robbie sealed Link within the Shrine of Resurection and then decided to separate in order to ensure one of them would survive long enough to assist Link when he finally awoke. Impa chose to remain at Kakariko Village, while her sister Purah and Robbie left the village. Purah constructed the Hateno Ancient Tech Lab in the East Necluda region where she continued her research into upgrading Runes, while Robbie constructed the Akkala Ancient Tech Lab in the Deep Akkala region where he had to defeat a few Guardians and continued his research in order to develop high-tech weapons and armor to assist Link in the future.
The final stand of the Hyrulean Soldiers
Although Ganon was sealed and the Divine Beasts became dormant, the Guardians and monsters continued to roam the land. The remaining Hyrulean Soldiers and Knights of Hyrule that survived the fall of Hyrule Castle relocated to the Akkala Citadel where they made their heroic final last stand against the Guardians but were defeated. Link was thus the only surviving member of the Knights of Hyrule and the armies of Sheikah, Gerudo, Gorons, Rito, and Zora were the only remaining military forces left to defend Hyrule.
New problems arrise
However without the Royal Family to lead them, these races became focused on protecting their own people and territories from the monsters roaming the kingdom due to Ganon's influence. The Sheikah also had to contend with the rival Yiga Clan a group of rogue Sheikah who served Ganon due to the mistreatment of their ancestors by the kingdom of Hyrule in the 10000 Years of Peace.
A new age of prosperity
Impa continued to lead the Sheikah who remained loyal to the Royal Family and eventually sent Symin to Purah and Jerrin to Robbie in order to assist them with their research. With Ganon under seal, the people of Hyrule began rebuilding in the aftermath of the Great Calamity. Hateno Village which survived thanks to Link and Zelda's actions during the battle at Fort Hateno was rebuilt. Uma who was born in Hateno Village during that period, spent her time to study the plants budding around the village, and the villagers had become self-sufficient.
However despite the relative peace, the Guardians and monsters continued to roam the lands of Hyrule attacking anyone foolish enough to come into their territory. Any slain monsters were revived when Calamity Ganon's power reached its peak at midnight during a Blood Moon. While Calamity Ganon remained mostly under seal, Hyrule Castle had basically fallen under his control with portions of it covered by his Malice, and various areas in and around the castle patrolled by his minions. As a result, places like Hyrule Castle and the Hyrule Castle Town Ruins became no man's lands. While most of the people of Hyrule chose to remain in the relative safety of villages and settlements such as stables, others became travelers who braved the dangers throughout the lands in search of adventure. The Great Deku Tree and the Koroks continued to stand guard over the Master Sword which had been entrusted to them by Princess Zelda. Meanwhile the spirit of King Rhoam watched over Link as he slept within the Shrine of Resurrection, while Zelda continued to keep Ganon under seal for one hundred years.