The Union of Soviet Socialist Republics was a country that existed in Earth's 20th century, stretching across Europe and Asia. Known by the abbreviation USSR, as well as the shortened name "Soviet Union", the country was dissolved in the 1990s, but existed in some form by the later half of the 24th century. (VOY: "Future's End"; TNG: "The Naked Now" dedication plaque) Along with the United States of America, the USSR was involved in mankind's earliest space exploration.
Government and regions
The USSR was a communist country and, between the 1950s and 1980s, a major rival of the United States of America. The USSR itself spanned across two continents and was comprised of a number of "soviet republics" such as Russia. Major cities included Moscow, Minsk, and Kiev. (TOS: "The Cage", "Wolf in the Fold"; VOY: "Future's End"; DS9: "What You Leave Behind")
Joseph Stalin was the dictator of the USSR during World War II. Although the USSR maintained the Molotov-Ribbentrop Pact with Adolf Hitler at the onset invasion of Poland, it was later invaded by Germany. Hitler was then forced to fight a two-front war in order to stave off the two superpowers, which he finally lost early in 1945. (TNG: "Manhunt"; ENT: "Storm Front, Part II")
In an alternate timeline created during the Temporal Cold War, the USSR was never formed because of the mysterious assassination of Vladimir Lenin in 1916. Russia still suffered an invasion from Germany in the 1940s, although Germany was able to easily capture Moscow since the alternate Russia "wasn't a threat" as compared to its USSR counterpart. (ENT: "Storm Front, Part II")
After the war, tensions between the United States of America and the USSR led to the Cold War. When Quark traveled back in time to 1947, he tried to play the Cold War rivals against one another, telling the American general Denning that he would sell Ferengi technology to the Soviets if the United States did not buy it first. (DS9: "Little Green Men") During the Cold War, the Soviet Union built villages similar to American villages to train operatives to infiltrate the United States. (VOY: "In the Flesh") The Cold War was eventually seen as a prelude to World War III, in particular after the Soviet Union tested its first H-bomb, which made headlines in US newspapers in the year 1953. (DS9: "Far Beyond the Stars")
On October 4, 1957, the USSR launched the first artificial satellite, the Sputnik probe. This turned the attention of the Vulcans on Humanity's development. (ENT: "Carbon Creek") Soviet space expansion continued over the next several decades. In 1968, as part of the nuclear arms race, nuclear warhead platforms were launched into orbit by all the major powers on Earth. The sabotage and subsequent detonation of the US suborbital warhead eventually led to a stronger international agreement to ban such weapons. (TOS: "Assignment: Earth")
This relative time period was used in the plot for the 24th century holoprogram, Julian Bashir, Secret Agent, where the Soviets were suspected by MI5 of being involved in the disappearance of three agents working for Great Britain in West Berlin. (DS9: "Change of Heart")
The USSR dissolved in 1991. (VOY: "Future's End") Among the last leaders were Leonid Brezhnev and Mikhail Gorbachev, the latter of whom met with American President George H.W. Bush. (ENT: "Storm Front, Part II")
The starship VK Yuri Gagarin, the USS Enterprise-D shuttlepod Tereshkova, and the USS Voyager shuttlecraft Tereshkova were named after famous Soviet cosmonauts. According to the Star Trek Encyclopedia, the Soyuz-class was named after the Soyuz spacecraft of the Soviet space program. The Korolev-class was named after the Soviet space pioneer Sergei Korolev.
The real-world reason behind the "USSR" being written on the dedication plaque is that no one foresaw the fall of the Soviet Union during the making of "The Naked Now" in 1987. The 1988 novel Ghost Ship, the first TNG novel, also had the Enterprise-D encounter a strange creature that had attacked a Soviet aircraft carrier in 1995. The Soviet name for Saint Petersburg, Leningrad, was also mentioned in several Star Trek: The Original Series episodes and in the 1986 film Star Trek IV: The Voyage Home, suggesting that the USSR existed again already in the 23rd century.
Pavel Chekov serves as a representative of Soviet Union in TOS. His frequent references to Leningrad and comically erroneous claims, can be seen as a satire of the Soviet Union's isolation from the western bloc in the mid-20th century when TOS was filmed.
The USSR, and its antagonistic relationship with the US, were the original inspiration for the Klingon Empire and its relationship with the Federation. The end of the USSR also served as inspiration for the events of the film Star Trek VI: The Undiscovered Country, during which many Soviet Republics had declared independence from the Union. (Captains' Logs: The Unauthorized Complete Trek Voyages, pp. 137-138)