The mitzva of the four species is connected to the joy of Sukkot, as we read, “On the first day you shall take the fruit of a hadar tree, branches of palm trees, boughs of dense-leaved trees, and willows of the brook, and you shall rejoice before the Lord your God seven days” (Vayikra 23:40). The Sages explain that the joy in taking the lulav (which represents all four species) is related to both aspects of the Ingathering Festival – the material and the spiritual.
The material milestone celebrated is the end of the ingathering of all the year’s produce, when people experience abundant joy. To sanctify and connect this joy to recognizing the One Who created and sustains the world, we are commanded to take the four species as a symbol of our gratitude to God (Ramban on Vayikra 23:39; Sefer Ha-ḥinukh §324). The Sages ordained the shaking or waving of the four species upward, downward, and in all four directions, to express our faith in the Lord of the heavens, the earth, and everything in all four directions. It also conveys an implicit prayer for the upcoming year: May our crops flourish, and may God save us from harmful weather (Sukka 37b; below, 5:4).
The spiritual aspect of the celebration relates to our completion of the process of repentance for the past year’s sins. Waving the lulav is waving a banner to signify victory, for the success of our repentance and our drawing closer to God. The Sages compare this to two litigants who presented their cases in court. At the conclusion of the trial, no one knew who had won. Only after one of the litigants waved his sword did everyone know that he had won. Similarly, each year during the Days of Awe, the wicked of the world accuse Israel, claiming that they have not been fulfilling their mission, do not deserve to represent God in this world, and are not even worthy of preserving. The deliberations are tense, and no one knows whose claims prevailed – until Israel emerges holding their lulavim and etrogim, signifying that they prevailed, that they are God’s children and people. The nations of the world even celebrate with them, which is why we offered sacrifices on their behalf on Sukkot. This is why we were commanded, “On the first day you shall take” (based on Vayikra Rabba 30:2; Zohar I 221a).
The Sages also said that the four species tied together allude to the four types of Jews who must unite in serving God. Their unification sanctifies God’s name in the world (as elaborated in 4:2-3 below) and also leads to great joy. Thus, by taking the four species, we can rejoice before God for seven days.