>>2808163Touhou 16 explains this. Spoiler warning:
In the story, a secret god named Okina Matara is lookin for new servants to replace her old ones, Mai Teireida and Satono Nishida. Okina does this by opening doors on the back of people and drawing their hidden powers forth. Because fairies control the nature of Gensokyo, the seasons go out of control.
Because a door opens on Cirno's back too, she feels empowered and decides to go beat up people. After beating a butterfly fairy, Eternity Larva, a mountain hag, Nemuno Sakata, the Hakurei Shrine's Komainu guard, Aunn Komano, and a jizo statue, Narumi Yatadera, she comes across a weird door behind jizo's back and an even weirder dancer.
After following the dancer, Mai Teireida, into a weird known as "the backdoor world" Cirno fights against Mai and her partner Satono. After a quick fight, the pair is called by their master and disappear. After rampaging for a while, Cirno comes across the secret god, Okina Matara, who tells Cirno that her mysterious tan was a side-effect from the door, Okina had put on her back, and the power leaking through was corrupting Cirno. Enraged Cirno fights Okina, and escapes after realizing that its hopeless for her to win.
Later Cirno returned to the Backdoor World through the door on Eternity Larva's back with new powers being drawn from her newly opened door. After a rematch with Okina and her servants, Cirno manages to win against them. Surprised by fairy's power, Okina grants Cirno a chance to become her servant which she refuses.
