The history of this mitzvah is less clear than the other mitzvot of Sukkot, but its performance is described in the Talmud (Tractate Sukkot 44a). Actually, it is written therein that "the [beating of] the willow branch and the water libation [ceremony] were given to Moses at Mount Sinai.” The fact that the ceremony continued after the destruction of the Temple and outside the land of Israel is considered to be of Prophetic origin.
The performance of the seven hakafot (circles around the bimah) and the beating of the willows is universal, whether one is Ashkenazi or Sephardi - although there are different customs as to when in the service they are performed. Following the hakafot of the hoshanot, a bundle (although a single branch may be used) of willow branches* is taken and beaten five times on the floor.
Because the origins of this ceremony are so cryptic, the meaning of beating the willow branches is the source of great conjecture, ranging from a connection to the Sukkot prayers for rain to an association with humility.
*The bunch of willow branches is also referred to as hoshanot.
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