The Waffen-SS was part of the Schutzstaffel (SS). "Waffen-SS" means "Armed SS" or "Armed Elite Guards" in German. The Waffen-SS was a paramilitary organization within the SS.
The divisions of the Waffen-SS were made of highly trained soldiers. Their original job was to protect higher-ranking people in the SS and the Nazi Party but later the Waffen-SS became a fully fledged military unit. Together with the Sturmabteilung ("Storm Battalion," or SA), they were used as a paramilitary police force.
In 1937, some soldiers were reorganized and nazi leaders gave some SS members the job of guarding and running concentration camps (and, later, death camps). These soldiers were moved from the Waffen-SS to the SS-Totenkopfverbände. But a main time the totenkopfverbände are a part of the SS too.
In some of the concentration camps, like Auschwitz and Buchenwald, doctors of the Waffen-SS did experiments on humans.
Heinrich Himmler led the SS from 1929 until Nazi Germany lost World War II in 1945. After World War II, the SS were found guilty of crimes against humanity, and the SS was completely abolished.