Mystery Spot (ミステリースポット Misuterīsupotto) and Power Spot (パワースポット Pawāsupotto) are a concentration of spiritual energy, often found in the Outside World, where the paranormal is likely to occur.
Power Spots are derisively referred to by Kanako Yasaka as quick, convenient places where one can go to temporarily gain power. While having the potential for spiritual training, they're almost never used that way, but rather for a quick "power-up" due to the nature of Outside World humans who no longer believe.
Mystery Spots are where ghosts actually do appear, some even traveling from Gensokyo and the Netherworld to visit. It is proposed that the Great Hakurei Barrier does not actually have much effect on them, allowing them to travel freely. Well-known haunted Mystery Spots, like cemeteries, hospitals, and schools often wind up as tourist attractions where Trial of Guts are held. Uninhabited shrines and temples also tend to make for ideal Mystery Spots.
The Secret Sealing Club has particular interest in the paranormal activity of these Mystery and Power Spots. A book about Japan's Power Spots exists, titled Japan's Power Spots Encyclopedia (日本のパワースポット大全。).