The Beis Yosef (651) brings the following story:
"In a dream, the Rikanti saw HaRav Yitzchak Ashkenazi writing Hashem's name, but he wrote the final heh slightly apart from the first three letters. The Rikanti didn't know the meaning of the dream. The next day, he saw Rav Yitzchak holding the esrog apart from the lulav. Then, he understood the meaning of the dream. He told Reb Yitzchak Ashkenazi that the four minim represent the four letters of Hashem's name, with the esrog representing the final heh. One must hold them together so that Hashem’s name be connected."
We tell this story to help us understand the mitzvah's holiness. Holding the four minim is like holding Hashem's holy name in our hands.
The Sar Shalom of Belz zy'a adds that although the four letters must be near each other, some space is required between them. This is why we use koisheklach (lulav holders). They serve as a divider between the four minim.
The Midrash (quoted in Ramban Vayikra 23:40) states: "The esrog is Hakadosh Baruch Hu, as it states... The lulav is Hakadosh Baruch Hu, as it states... Hadassim are Hakadosh Baruch Hu... The aravos are Hakadosh Baruch Hu..." Keviyachol, when we hold the four minim, we hold Hakadosh Baruch Hu Himself. We don't know exactly what that means, but it reveals just a drop of the holiness of the mitzvah and the privilege we have to perform it.
Based on these ideas, Rebbe Naftali of Ropshitz zy'a explains the pasuk, אירא לא לי 'ה. He teaches, לי 'ה, "Since Hashem is with me [as I hold the four minim] אירא לא, I have nothing to fear."
Reb Shimon Deutsch zt'l (Imrei Shefer) writes, "My teacher, the Chasam Sofer zt'l, would [hold the four minim throughout the entire tefillah]. He explained that he loved the mitzvah and that holding the four minim helped him daven with greater kavanah. The Chasam Sofer said he has more kavanah on Succos while holding the four minim than on Yom Kippur."
The Midrash teaches that the four minim represent the human body: The esrog represents the heart, the lulav the spine, the hadasim the eyes, and the aravah the mouth. The Chidushei HaRim zt'l explains that when you want to awaken someone, you shake them. Similarly, we shake the four minim, which represents the person, to awaken him to ruchniyus. We don't need to take the four minim on Shabbos because Shabbos awakens us.
The Shevet Mussar explains that yavesh (dried-out esrog and lulav) is pasul because one needs to be fresh and alive when serving Hashem, not shriveled up and dry. And, indeed, that is the segulah of the four minim – to awaken us so we can serve Hashem with a chiyus and vigor.
