The Gotoro Empire is the opposing force that is fighting against the Ferngill Republic, in which Stardew Valley is located. Not much else is known about the empire other than a few villagers mentioning the existence of the opposition.
The Traveling Cart merchant claims that the items she has have been smuggled from the empire as well.
Kent, who returns in Spring of Year 2 after fighting overseas, will describe how dreadful it was in a Gotoro prison camp when you gift him something he hates, as that item was also given to him in the prison camps. Another mention of the empire is when Kent's son Sam tells you about his father before he actually returns to Stardew Valley through regular dialogue.
|“||“My Dad is a soldier, fighting against the Gotoro Empire. That's why he's not here. He'll come back someday.”|
|“||“I've heard some terrible things about the Gotoro Empire.”|
|“||“Dad was telling me about our national enemy, the Gotoro Empire... They sound like a ruthless bunch.”|
The Gotoro Empire is located south of the Gem Sea. The Beach, south of Pelican Town and where Willy's fish shop is, serves as the shoreline for the Gem Sea. It can be assumed that The Gotoro Empire is south of this area.