Welcome to the fascinating world of Gensokyo, in which youkai (A term for all sorts of spiritual creatures), animals and some humans live, completely separated from our world by a magical barrier. The only gateway between the two worlds is the Hakurei shrine.
Reimu Hakurei is the maiden working at said shrine. Whenever problems of supernatural causes (known as “Incidents”) occur, Reimu goes out with her friends to investigate, eliminate the cause and hopefully restore Gensokyo to its equilibrium.