It also recognises that His grace and bounty benefit every part of His Creation.
These are amongst the best-known interpretations of the mitzvah.
In an additional comment on a Talmudic passage, the Tosafot (Suk. 37b) gives it a messianic connotation.
It sees the waving lulav as a symbol of the wind blowing through the plants and trees, quoting the words we know from the Shabbat evening service, “Then shall all the trees of the forest sing before the Lord when He comes to judge the earth” (Psalm 96:12).
In similar fashion, the Midrash asks why God instructed Israel to wave the lulav and says that when God took Israel out of Egypt (Psalm 114) “the mountains skipped like rams”; similarly, when the time comes for Him to bring redemption to all mankind, the mountains and hills will leap forward in their delight and all the trees of the forest will sing with joy.
We shake the lulav to show our yearning for the messianic age and to remind God of His promise.
This is one of the reasons why Sukkot is called in rabbinical literature he-chag, the festival, because it not only reminds us of our history, when little ramshackle huts protected our ancestors from the buffeting of the elements, but it foreshadows our future, when all mankind will sit in unity in God’s universal sukkah and call upon the One Eternal God, and every part of the universe will acclaim the grandeur and power of its King.