What was the purpose of Nazi concentration camps like Auschwitz, Treblinka, Belzec, Sobibor, and so forth?
First of all, Treblinka, Belzec, Sobibor and Chelmno were not concentration camps. They were “death camps” (“Vernichtungslager” in German). In those camps, the only purpose was to murder Jews. They were almost always gassed within a short time of arrival and very few were chosen to perform slave labour, such as was the case in Auschwitz. As an example, only about 7 Jews survived the Belzec extermination camp, although at least 550,000 were killed there. Auschwitz was a complex of camps; some Jews were killed in Auschwitz I (the main camp), but most were killed in Auschwitz II (Birkenau). Auschwitz III (Monowitz) was involved with production of synthetic rubber and other materials. In addition, there were literally thousands of concentration camps where people were imprisoned, often under hideous conditions. But their intent was not primarily murder for its own sake.
The Nazi concentration camp system served as a source of labor and income for the SS which rented prison labor to private industry. It was a prison system for common criminals and political enemies. Auschwitz and Birkenau held many unemployed prisoners, many of them with no job skills or too sick to work. These included inmates with chronic illnesses such as tuberculosis. Some camps were designated transit camps where Jews being resettled in ghettos in the East were deloused before being sent on to their final destinations. In some cases Jews were placed in quarantine before being sent to their final destinations to prevent the introduction of diseases like typhus into the Eastern ghettos. This is not to say many Poles, Gypsies, and others did not die in the Nazi concentration camps. They did, but the context of their deaths is quite different than the one usually portrayed.