She is the miko of the Hakurei Shrine, a remote building far in the east where the boundaries of Gensoukyou and the human world overlap. It is believed that she is the 13th of her line.

Reimu is very easygoing—some would say lazy—and hates to train. As such, even though she's naturally talented, her offensive and magical abilities are only average. However, she has a strong sense of duty, and if it's for the sake of Gensoukyou she can overcome almost any obstacle through sheer perseverance.

Her main abilities are to "fly", good intuition, and getting along with everyone; even those who were once her enemies. In the games, she is characterized by her homing amulets and yin-yang orbs.

Her ability to fly should not be confused with the ability to "float" possessed by most characters in the Gensokyo Universe. In Japanese, the translation for "fly" could mean "to be isolated from others," "to be uncertain/undefined," "to have no basis," and finally "to float." For example, in Eastern and Little Nature Deity, Chapter 2, Reimu successfully walks across a magically dissimulated river without even knowing it exists.

Basically, it is assumed that Reimu's ability to "fly" could be translated to floating, and as if it were not defined in the world, having no basis and even passively doing things that are considered impossible by nature and can only be explained this way.

(Source: Wikipedia)