Over five hundred years ago, the Inca residents of the area around Arequipa were suffering from poor harvests. The reason, they believed, was that their gods were angry that they had no received the proper veneration. To appease them, the Incas brought a young girl of noble blood to the volcano of Ampato and sacrificed and buried her at its summit. This museum amply explains why the Incas made a sacrifice, why they chose a young girl (nicknamed Juanita), and why they chose to sacrifice her on a mountain.
While you should certainly visit if you're in Arequipa, the reasons are relatively easy to explain. The Incas believed that their gods, both the earth mother (Pachamama) and the mountains (known as apus) periodically required human sacrifices in order to guarantee good harvests. The Incas sacrificed children, usually (but not always) girls and typically of noble birth, because they were considered pure. While the concept of being forced to hike up a mountain in sandals, then being drugged and killed is unpleasant, it was supposedly considered an honor by the victims who then became immortal (although since the Incas didn't have a system of writing and the children didn't live to tell their side of the story this is something of a conjecture.) The sacrifice took place on top of a mountain because it was a sacrifice to the mountain.
There's much more to Inca religion than this bare recitation of facts, and through an introductory video and an hourlong guided tour (usually in English), this museum amply explains much of it. The guides do so by making reference to many objects found at Inca sacrificial sites in the area, including Juanita's garments. Pride of place goes to Juanita's corpse itself, although it is rotated with that of other child sacrificial victims found in the area in a specially cooled chamber. The corpses were only discovered in the late 1990s after volcanic eruptions near Arequipa caused the snow on nearby mountains to melt, which allowed archaelogical expeditions to ascend the peaks. Technically speaking, the corpses are not mummies since they were preserved by the cold rather than by binding or chemical techniques.
Regardless of whether you find the aforementioned summary fascinating or revolting, the museum itself is interesting, both for the story that it tells and the sheer beauty of many of the objects displayed. In particular, Juanita's coat is so well preserved that you can still see the blood spots from the single death blow that she received. On a slightly more pleasant note, the small precious sculptures of llamas buried with the victims are as exquisite as any I've seen in any of Peru's fine archaeological museums. I highly recommend a visit to this museum to get a sense not only of Inca religion, but also of the culture's relationship with the mountains that encircle Arequipa.