The days of Sukkot were special days of happiness in our Bet haMikdash (TVTB'B)
In addition to the Biblical commandment of taking the four species to rejoice on Sukkot, there were also two other commandments fulfilled in the Holy Temple during Sukkot. These two practices are not mandated by the Scriptures; they are included in what is called halakha leMoshe miSinai - religious traditions that God taught to Moses at Mount Sinai. One of these two items is the 'commandment of the willow' (see link for the second Mitzva).
The commandment of the willow is not to be confused with the 2 arabot, the willow branches that are included in the four species, tied together with the lulaband myrtle.
For this willow branch of the Mosaic tradition is a different practice altogether and exclusively associated with the Holy Temple:
There was a place at the foot of Jerusalem called Motza (there is a suburb in Jerusalem's outskirts called Motza to this day). Each day of Sukkot, the people would descend there and cut down huge willow leaves. These branches were exceptionally long -their height reached 5-6 meters. The people would place these branches all along the foundation of the altar, with their heads bent over the top" (Sukkah 4, 5).
Since the altar itself was 5 meters high and the branches measured up to average 5.5 meters, a
length of one amah (approx. 0.5 m) would hang over the top of the altar on all four sides. This was the essence of the oral commandment that Moses received at Mount Sinai... to place these arabot around the altar.
Each day of Sukkot, willow branches were arranged firmly along the altar's foundation. The priests would march one time around the altar, making a circle with their lulavim in hand, appealing to the Almighty "We beseech You, O L-rd, please save us! We beseech You, O L-rd, please grant us success!" (ana haShem hoshia na; ana haShem hatzlicha na).
On the last day of the festival, the seventh day, they would "surround" the altar seven times-as a remembrance of the conquest of Jericho (JT Sukkah 4, 3).
Adapted from the Temple Institute of Jerusalem (Machon haMikdash)
See the second special mitzvah of Sukkot (nisukh hamayim):http://www.templeinstitute.org/archive/water_libation_festival.htm