Showa Era refers to the Japanese history time when Suzuno Osugi was inside The Universe of the Four Gods, following the Taisho Era. The era's end also marks the summoning of the beast god Byakko, along with the tragic separation of Suzuno and Tatara.
The Showa Era coincides with the reign of Emperor Showa, better known to Westerners by his birth name Hirohito, who was in the throne from December 1926 to his death in January 1989. Socially and politically speaking, the Showa Era is marked first by the Japanese Empire's cruel, iron-fisted colonialism and expansion through South-East Asia and its extremely conflicted role in World War Two, and from 1945 on by the rebuilding of the country after both the atomic bombings and the American occupation. In fact, when Byakko Senki's plot truly begins to move, Japan had already begun to extend its control through Asia, and had just seized Manchuria (in Northern China) to make it into the puppet state of Manchukuo.
Suzuno's adventures properly began in the Taisho Era, more exactly in 1923: her 8-year-old self was sent to the Universe of the Four Gods right after the Great Kanto Earthquake that destroyed Tokyo, returning to the ruined city few hours (book)/days (real world) later.
Suzuno's actual adventures in the book, however, begin in the seventh year of the Showa Era, sometime in 1933. In these days, she is 17-18 years old and in her last year of high school, and has lived with her adoptive father Oikawa and three boys named Seiji Horie, Hidero and Kenichi. Seiji, the eldest of the four kids, has entered the Imperial Japanese Army Academy (Rikugun Shikan Gakkou) for two reasons: to help Oikawa support their adoptive family, and to make research about the Universe of the Four Gods. This is because back then there was heavy censorship in Japanese media about anything regarding China, the country where Einosuke Okuda found and translated the book itself.