Avatar: The Last Airbender told a complex, sweeping and heartfelt story in the span of just three seasons. The first season, called "Book One: Water," launched Avatar Aang's story, but this was only the beginning.
Following this was "Book Two: Earth," and here, Aang was determined to master both the Avatar State and the element, earth. The Gaang trekked across the Earth Kingdom to find some leads, but what Aang didn't realize was that somewhere out there, Zuko's redemption arc had begun and a new threat was emerging.
When Princess Azula Declared Zuko & Iroh Fire Nation Fugitives
Prince Zuko had been the main villain in Book One, but in Book Two, he goes his own way. His redemption began when he and Iroh became enemies of the Fire Nation. Princess Azula arrived, under orders to capture Zuko and Iroh. Only narrowly did Zuko and Iroh escape, so Azula spread the word: Zuko and Iroh were fugitives of the Fire Nation.
This helped convince Iroh that the Fire Nation was truly lost and that he and Zuko could gain nothing from it. The two of them learned to rely only on each other, and Zuko took this chance to learn much from his uncle. Without his mission to capture the Avatar, Zuko became far more receptive to Iroh's teachings while on the run, and they even ended up in Ba Sing Se together.
When Toph Ran Away From Home To Teach Aang Earthbending
Looking back, it seemed obvious that only Toph Beifong could be Aang's earthbending teacher, but at the time, Toph's style was rather unconventional compared to other Earthbenders. Aang already knew King Bumi from his childhood in the pre-war days, but Omashu fell to the Fire Nation, and so Bumi told Aang to find another teacher who mastered the "wait and listen" aspect of earthbending.
In the end, only Toph Beifong could teach Aang these fundamentals, as she could only "see" via earthbending and learned this from badger-moles. Toph was a wild child who refused to help at first, but she changed her mind and resolved to teach Aang. All this added much-needed depth to the philosophy of earthbending. Later, Toph would discover that metal is a part of the earth, so it could be bent as well.
When Sokka Learned About The Day Of The Black Sun
At one point, Sokka wanted to visit a long-lost library. This buried library, belonging to the owl-like spirit Wan Shi Tong, had a vital clue on how to defeat the Fire Nation. Sokka learned about the mysterious "day of the black sun," referring to the solar eclipse. During Wan Shi Tong's angry rampage, Sokka frantically used the planetary calendar to determine which day the eclipse would take place.
Sokka got his answer, and he and the group narrowly escaped before Wan Shi Tong sank the library underneath the desert sands. The group had the edge on the Fire Nation, and an invasion would be launched later in "Book Three: Fire."
When Azula & Long Feng Overthrew Earth King Kuei
Aang and his friends entered Ba Sing Se to get the king's support in the war and find Appa. However, despite the failure of her giant drill, Azula was determined to take this city down, and she did from within. She, Ty Lee and Mai disguised themselves as Kyoshi Warriors to earn King Kuei's trust, and Azula consorted with the scheming Long Feng to take Kuei down.
Incredibly, Azula not only took down the king, but she also vanquished Long Feng. This coup brought about the Earth Kingdom's downfall, and the war was all but over. Plus, the Day of Black Sun invasion would have to proceed without substantial Earth Kingdom help.
When Zuko Sided With Azula Against Aang
During Book 2's climax, all major parties met in the catacombs underneath Ba Sing Se, where Zuko found himself torn between his uncle and Azula -- who promised to restore Zuko's status in the Fire Nation. By now, Zuko's redemption arc was already underway, but he was not yet ready to realize his destiny. He needed to personally see how twisted the Fire Nation had become.
Only then did he resolve to side with Aang, take down Ozai and reform the Fire Nation. So, for Zuko's sake, it was essential that he sided with Azula over Iroh here. Zuko's regret over this decision also helped bring out his good side later on.