The Hakurei Yin-Yang Orbs are orbs with the appearance of the Yin-Yang symbol. They appear next to Reimu Hakurei in several games and are used in many of her attacks, either as danmaku or as part of her Spell Card. Based on the Prologue to Highly Responsive to Prayers, it seems that the orbs are a weapon belonging to the Hakurei Shrine. Reimu seems to be only the latest person to wield this weapon, "the Hakurei Shrine's greatest treasure." Originally, they were her only real means of damaging enemies. Additionally, according to Mima, only a bloodline member of the Hakurei clan can properly use the orbs. Since Reimu is the only known living member of her clan in Gensokyo, she's the only one that can use them.
In Story Of Eastern Wonderland, depending on which ending you get Genjii will explain the orb's "true power", each of which is hilariously mundane and are never spoken of again.