Short answers, pulled from the story.
Left-bank Ukraine occupies the eastern side of the Dnieper River. Today, the region encompasses three full administrative oblasts: Chernihiv, Poltava, and Sumy. It also includes the eastern portions of Kyiv and Cherkasy oblasts.
The specific designation Left-bank Ukraine appeared in 1663 during a contentious political moment. Ivan Bryukhovetsky became the first known leader to hold the title of left-bank Ukraine hetman after winning an election against Pavlo Teteria.
Since the Middle Ages, the region formed part of several major empires that rose and fell across Eastern Europe including the Khazar Khanate, Kievan Rus', Mongol Empire, Golden Horde, Grand Duchy of Lithuania, and Kingdom of Poland. No single power held the land for more than a few centuries at most.
Local Cossack leaders swore allegiance to the Russian monarchy in exchange for military protection under the Treaty of Pereyaslav of 1654. Russian sovereignty over the area was later reaffirmed in the Treaty of Andrusovo on the 2nd of March 1667 and finalized by the Eternal Peace Treaty signed on the 30th of January 1686 between the Polish, Lithuanian Commonwealth and Tsardom of Russia.
This self-governance existed as the Cossack Hetmanate starting from 1721 when Imperial Russia took full form. Gradual withdrawal of this independence occurred throughout the eighteenth century until the destruction of the Zaporizhian Sich marked a turning point in this process.