Short answers, pulled from the story.
Kaliningrad Oblast is the westernmost federal subject of Russia, a semi-exclave on the Baltic Sea. It is bordered by Poland to the south, Lithuania to the north and east, and the Baltic Sea to the west, with no land connection to the rest of Russia.
Kaliningrad Oblast became isolated after Lithuania's independence in 1990 and the dissolution of the Soviet Union in 1991. The isolation deepened when Poland and Lithuania joined NATO and the European Union, meaning every land link between the region and the rest of Russia must cross NATO and EU territory.
Kaliningrad was called Königsberg, a city the Teutonic Order founded in 1255 in honour of Ottokar II of Bohemia. It was renamed Kaliningrad in 1946 after Mikhail Kalinin, the Chairman of the Presidium of the Supreme Soviet of the USSR, who had no connection to the city.
Kaliningrad Oblast holds roughly 90 percent of the world's amber deposits, which is why many Russians call it the Amber Land, or Янтарный Край. In 2013 the Russian government banned the export of raw amber to boost the domestic amber processing industry.
Kaliningrad Oblast had a population of 1,027,678 in the 2021 Russian census. Russians made up 78.6 percent of the population, with smaller communities of Ukrainians, Belarusians, Armenians, Lithuanians, Germans, and others.
Königsberg passed to the Soviet Union under the Potsdam Agreement of the 1st of August 1945, after the defeat of Nazi Germany in World War II. It was added to the Russian SFSR in 1946, the remaining German population was expelled between 1947 and 1948, and the area was repopulated mostly with ethnic Russians.