Short answers, pulled from the story.
The Soviet Union demanded that Turkey cede territory in eastern Anatolia including areas around Kars, Ardahan, and the Black Sea coast as far west as the town of Terme. Three separate plans outlined different scopes, ranging from the former Russian Empire oblast of Kars and Batum to a larger swath taking in Trabzon, Erzurum, Van, Mush, and Bitlis.
According to the memoirs of Nikita Khrushchev, deputy premier Lavrentiy Beria pressed Joseph Stalin to claim eastern Anatolian territory that had been annexed from Georgians and Armenians during the Turkish war of Independence.
When the 1925 Soviet-Turkish Treaty of Friendship and Neutrality expired in 1945, the Soviet side chose not to renew it. Foreign minister Vyacheslav Molotov told the Turks that Georgian and Armenian territorial claims would have to be resolved before any new treaty could be concluded.
In December 1945, academics Simon Janashia and Niko Berdzenishvili published an open letter in Pravda, Izvestia, Communist, and Zarya Vostoka demanding that Turkey return approximately 20,000 square kilometres of Black Sea coastal territory they described as ancient Georgian lands, including the regions of Rize and Trebizond.
The United States opposed Soviet annexation of the Kars Plateau on strategic grounds and viewed the claims as expansionist. Turkey joined NATO in 1952, and following Stalin's death in 1953, the Soviet government formally renounced its territorial claims against Turkey to improve relations with Ankara and Washington.
Western Armenia comprises a significant portion of the ancestral homeland of the Armenian people before the Ottoman forced deportations during the Great War. A large part of the Soviet territorial claims, particularly under the third plan covering Erzurum, Van, Mush, and Bitlis, corresponded to this region. Between 1946 and 1948, roughly 150,000 ethnic Armenians from the diaspora had already migrated to Soviet Armenia, and Moscow planned to resettle them in any acquired territories.