Role in the film
When the great bird was awoken from its hibernation state by the Spring Sprite, it unleashed a brutal and terrifying display of its destructive power on the Sprite's and Elk's home. It is unknown why the Firebird attacked the Sprite to begin with, but it can be assumed that it was enraged for being awakened, or it just felt the urge to begin a chaotic rampage. After the destruction was done, it returned to its slumber.
It shares a far number of similarities to Chernabog, the villain from Night on Bald Mountain in the original film. They both emerge from a mountain, they reek chaos, they can both manipulate fire, and good ultimately triumphed over both of them. It is interesting to note that they both appeared in the last segment of the two movies.
This interpretation of the Firebird actually conflicts with the original version of Igor Stravinsky's ballet. In the ballet, the Firebird was described as a benevolent, peaceful being who bore no traits of evil. However, Disney's Firebird was violent, destructive, and merciless, showing no qualms of destroying a newly-created forest.
Role in the series
The Firebird is currently sealed away in a different prison from the Banished Realms that is accessed from the volcano the Spring Sprite found him in. Malefor has sent Mirage many times to try and free this creature, but the Spring Sprite constantly prevents her from succeeding. It's only appearance was in the backstory of the destruction of Radiant Garden, and was the one responsible for doing most of the damage, and presumably the murder of Kairi's grandmother. As the Firebird was about to attack Mickey Mouse, who earlier interfered with the attackers, Lord Shen quickly decided that was enough bloodshed and attacked the Firebird with his cannons, though not destroying the beast, just briefly preventing it from becoming a further menace, allowing Mickey, Kairi, and Aqua to escape, but not without a very angry Cobra scolding Shen and restrengthening the darkness within him, and erasing his memories of Radient Garden and Kairi. In SpongeBob, Simba, and Friends Meet Bambi, the Firebird returns when Cobra summons it to assist Fagin and the Lodge in their final assault on Bambi, SpongeBob and the others while causing the forest fire along with Maleficent in her Dragon form.
It's also set to be a member of Deathwing's renegade villain team in the Jak and Friends series, though it only played a role of replacing the pink elephants as a hallucination.