The phrase "satellite nations" or "satellite states" refers to countries that the Soviet Union either seized at the end of World War II or were "granted" as part of the negotiated agreements among the United States, Britain and the Soviet Union. While they were ostensibly independent countries, including holding seats in the United Nations, they were by no means independent in practice. In fact, in several instances -- Poland in 1939, Hungary in 1956, and Czechoslavakia in 1968 -- the Soviet Army was dispatched to forcibly seize or retain control of these countries, with the invasion of Poland and the crushing of the Hungarian revolt being particularly brutal.
The phrase "satellite nations" was derived from the astronomical phenomenon of plants orbiting a central source of power, i.e., a star like the Earth's Sun. These planets are physically unable to break free of the star's gravitational pull, and are captured for eternity. That was Stalin's idea with regard to the countries of Central and Eastern Europe. The Baltic nations of Latvia, Estonia and Lithuania were pulled in early, along with eastern Poland (the Germans laying claim to western Poland until the invaded Russia and took the rest of Poland). The fates of Poland after "liberation," Hungary, Czechoslavakia, Romania, Bulgaria, Albania, and East Germany were all determined by the three World War II allies in preparing for a post-war world.
Russia, while a major player itself in the game of imperialism -- the Caucasus, Central Asia, Ukraine, and the Russian Far East were all forcibly incorporated into the Soviet Union -- nevertheless feared a resurgent Germany that could once again pose a military threat. In order to prevent such an occurrence, Stalin insisted during the Yalta and Potsdam conferences with the U.S. and British leaders that the Soviet Union be given control over the aformentioned countries. As the Red Army was militarily in control of these regions as a product of its drive to Berlin during the war, the U.S. and Britain acquiesced to the continued Soviet control of the satellite nations.
In addition to providing a buffer from a resurgent Germany, Stalin wanted control over the satellites for the resources they could provide in rebuilding Russia following the devastation of the war. Consequently, each of those captive nations spent the next four decades supplying Russia with manufactured goods that its own economy was not able to produce, as well as military forces -- under the aegis of the Warsaw Pact -- to assist in both defending the Soviet Union and in posing a military threat to Western Europe.