The Torah says that we are to wave the Luluv all seven days of Succoth in the Temple area, but outside the Temple area this commandment applies only on the first day of the Holiday.
However, the Rabbis have decreed that wherever we are, we are to fulfill the mitzvah of waving the Luluv all seven days of the Holiday.
The Rambam states that even today when in the Temple area waving the Luluv fulfills a Torah commandment and is not merely a rabbinic decree.
This is why we see so many religious Jews coming to the Kotel all week long, and even though they certainly waved their Luluvs in their neighborhoods in the morning, they borrow a set from someone to briefly wave them again (without reciting the blessing). Thus, in their neighborhoods during the week they fulfilled the mitzvah as a rabbinic mitzvah, and again, if they come to the Kotel and wave them a second time, as a Torah mitzvah.
It is both a privilege and a joy to be able to be there to help them.