By Rabbi Yair Hoffman for 5tjt.com
Some people do it. Some people, specifically, avoid doing it. The issue under discussion is placing the used up Aravos on top of the Aron Kodesh after davening on Hoshana Rabbah. What is the reason for this Minhag? There are apparently two reasons that are brought down for the Minhag to do it
Rav Yom Tov Lipman Bosliansky (1821-1892) the Av Beis Din of Mir Poland and the author of the Malbushei Yom Tov 669:1 writes that they are placed there at the end of the period of judgement because they are the leftovers of the hoshanos just as there are leftover aspects of judgement that occur at this time. The understanding of his words are not so clear, but it seems that his intent is that which is left over from our fulfilling of the Mitzvah of the hoashanos should stand us in good stead for all that is left to be meted out to us in justice.
Rabbi Reuvain Margolios (1889-1970), author of the Nitzotzei Zohar (in Parshas Tzav) writes that this is the source of the idea not to bring home the leftover Aravos because they signify the Attribute of Justice. This is why they are leftover in the shul.
USING THE SAME ITEM FOR A SECOND MITZVAH
Another reason, cited by the Kitzvur Shulchan Aruch, is that there is a concept in the Gemorah in Shabbos 117b that once a Mitzvah was done with an item that item should be utilized for another Mitzvah. Dried out Aravos (and lulavim for that matter) make good kindling fuel in which to burn Chometz six months later.
MINHAG TO BRING THEM HOME
On the other hand, the Kaf haChaim cites opinions that specifically do bring the Aravos home and do not place them on top of the Aron. The reasons are that it is a segulah to bring into the home something that was used for a Mitzvah. Otehrs seem to imply that it is not in the kavod of the Aron Kodesh to be placing something on it.