Short answers, pulled from the story.
A satellite state, or dependent state, is a country that is formally independent but under heavy political, economic, and military influence or control from another country. The term was coined by analogy to astronomy, comparing such a country to a small moon orbiting a larger planet.
Soviet satellite states of the Cold War included the People's Republic of Albania (1946 to 1961), the Polish People's Republic (1947 to 1989), the People's Republic of Bulgaria (1946 to 1990), the Romanian People's Republic (1947 to 1965), the Czechoslovak Socialist Republic (1948 to 1989), the German Democratic Republic (1949 to 1990), and the Hungarian People's Republic (1949 to 1989).
Mongolia is considered a Soviet satellite because, despite being nominally independent after the Mongolian People's Republic was proclaimed on the 26th of November 1924, it remained under heavy Soviet influence until 1990. It collapsed less than two months after the Soviet Union itself dissolved.
Albania broke ties with the Soviet Union in 1961 under Enver Hoxha, in what is known as the Albanian-Soviet split. Romania's de-satellization process began in 1956 and ended by 1965, following a final rejection of Soviet hegemony in 1964.
William Pfaff warned that a permanent American presence in Iraq would "turn Iraq into an American satellite state." John Pilger accused former Australian Prime Minister John Howard of turning Australia into America's 51st state, and North Korea has regularly described South Korea as a "puppet state" of the United States.
The Oxford English Dictionary traces the concept of satellite states in English back as early as 1780. The term was coined by analogy to planetary objects, comparing smaller moons orbiting larger planets to smaller countries dominated by larger ones.