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What purpose did the gulags serve in Russia?
The Gulags, apart for their basic finality of reclusion sites and forced labour reservoirs, had an innovative (even if somehow tragical) component of re-educational purpose.
The main difference between, say, a Nazi concentration Camp (lager) and a Soviet gulag was the fact that the inmates of a lager were not supposed to come out alive or come out at all while the inmates of gulags were there only for a period of time after which (theoretically) they could go back into society.
In Soviet Russia an inmate of a Gulag was there to spend a certain period of time (given through the emission of a sentence) because he was an ENEMY OF THE STATE. Although this definition seems normal, here it has an interesting twist. Inside the gulag the inmate had to learn about his or her "mistake" (a mistake that could be political, of thinking or of origin) and change to be able to go back into society. In the meantime the inmate had to work to sustain the "proletarian" struggle and contribute to his or her residence costs (normally in pointless but terribly punitive and harsh activities).
You can have a good idea of the lifestyle and struggle inside a gulag from the novel (also transposed into a movie with the same title):One Day in the Life of Ivan Denisovich by Aleksandr Solzhenitsyn
So, basically the Gulags were enormous prisons where you could be sent for any kind of reason to spend a more or less long amount of time working and learning how to be a good citizen. The main categories of inmates of the gulags (in a kind of temporal sequence) were:
1) Nobles and old Czar functionaries or White Russians (counter revolutionary activists and soldiers); these normally wouldn't survive long in the environment of violence and extreme insalubrity of the camp.
2) Rich people such as landowners, industrials and merchants;
3) Kulaks; small land owners supposedly richer than the other peasants. Stalin in particular had something against them and they became a kind of Jewish counterpart, as they were for the Nazi, of the Soviet Regime.
4) Normal criminals; although these had special camps for them sometimes they were mixed in other camps as to toughen up a bit the environment;
5) Political; these are very difficult to categorize in particular under Stalin's regime where EVERYBODY could be a counterrevolutionary agent or conspirator. They were the big chunk of the inmates and their fall could be caused by simple things as neglecting a simple duty, being the descendent of an old regime person (possibly czarist), having travelled to a foreign country, being Jewish or religious or making a joke about the leaders. Consider that most of the leaders, in turns, would become inmate of gulags themselves!
6) War prisoners; these came late in Soviet Russia and are mainly Germans or allied captured during World War II or "collaborators" (most soviet soldiers captured by the Germans and released at the end of the war were labelled collaborators and simply switched a German lager for a gulag).