GULAG (Glavnoe Upravlenie Ispravitel-no-trudovykh Lagerei, "Chief Directorate of prison camps") is an acronym for the administration of the Soviet prison labour camp system, and an archipelago is, of course, a chain of islands. The idea is that the system of labour camps which was spread across the Soviet Union under Lenin, Stalin and their successors, was a vast region known only to those who were fated to visit it.
Solzhenitsyn originally wrote the book in secret after his own term as a political prisoner, but he had it published abroad in 1973 after the KGB (Soviet secret police) confiscated a copy of the manuscript.
The unrelenting detail of the book, which presented information on the putative crimes and criminals, their phony trials, the transportation and treatment of prisoners, all in the context of a long history of oppression dating back to Lenin's absorption of the Tsarist security apparatus, forced the West to acknowledge directly the totalitarian nature of the Soviet state.