And you shall take unto yourself on the first day…
According to the Midrash, the festival of Sukkot is considered the first day in the calculation of sins. Why? On Yom Kippur, the 10th of Tishrei, the slate was wiped clean.
For the next few days, the 11th through the 14th, every Jew is busy eagerly preparing for the holiday. The first day of Sukkot, on the 15th, is the first opportunity an individual could have possibly had to commit a sin! Furthermore, according to some opinions, the fruit of the Tree of Life eaten by Adam and Eve in the Garden of Eden was an etrog. The first day of Sukkot therefore marks the beginning of the calculation of sin for all mankind.
(Kerem Hatzvi)
And the feast of ingathering, at the end of the year, when you gather in your labors out of the field. (Ex. 23:16)
After you have gathered in the bounty of the land, and your homes are filled with all manners of goodness - corn, new wine and pure oil - you shall dwell in sukkot, in order to remember that for forty years I sustained you in the desert. With this in mind you shall give thanks for your inheritance and for your houses full of plenty; do not say in your heart, "my power and the might of my hands have wrought this strength."
(Rashbam)
And you shall rejoice in your festival and be happy - "ach sameach" (from the holiday Torah reading)
Without certain boundaries, unrestrained rejoicing can lead to levity and frivolousness. By using the word "ach" (literally, "but"), the Torah cautions that even while we rejoice, we must always be conscious of the reason for our rejoicing.
(Sefat Emet)
Lulav
The word "lulav" is comprised of two Hebrew words - lo (to him) and lev (heart), to teach us that a person must always strive to subjugate his entire heart to "Him" - to the Holy One, Blessed be He.
(the Alter Rebbe)