Thunder Brew was first mentioned when Amaterasu needed to get sake from Kushi for Susano. Kushi mentioned giving a monster some Thunder Brew, which made the monster broke her waterwheel which she needed to polish the rice for sake.
Thunder Brew was next mentioned on the night of the Kamiki Festival. Susano drank all the 8 Purification Sake, so Kushi instead decided to take the Thunder Brew with her to intoxicate Orochi when she is chosen as its sacrifice. When Orochi grabbed Kushi at the entrance to the Moon Cave, she took the sake in with her. She then dropped it and it somehow ends up in the Calcified Cavern. Amaterasu and Issun retrieved it, intending to use it to intoxicate Orochi.
During the confrontation with Orochi, Issun threw the sake at Orochi, who drank it. However, it had no effect whatsoever, and Orochi just spitted the bottle onto the floor. Just when it seemed all hope is lost, Susano appeared to face the monster. Susano's renewed faith triggered a key event: the Thunder Brew became the 8 Purification Sake and started pouring out of into the moat on the floor. It was then used to defeat Orochi.
Later, during the Kamiki Festival, Kushi gave the Thunder Brew to the villagers in place of the 8 Purification Sake.
Spoilers end here.
At the Kamiki Festival, Karude, Mr. Bamboo, and Nameless Man can be drunk if Waterspout is used on them with the Thunder Brew, which shows how powerful the sake can be. Oddly, there is an electric effect similar to Thunderstorm seen when the sake is taken out of the barrel using Waterspout. Mushi and Kokari can also be struck down by the sake, but they will not get drunk and will instead fall down and then start running around again. This does not work with the barrel of Thunder Brew Mr. Orange, Mrs. Orange and Mushi's Mama are drinking from.