In what way are all six hundred thirteen mitzvos dependent on the mitzvah of succah?
Rabbi Bunim of Pshis'cha said, "The mitzvah of succah is so precious - because I enter into the mitzvah with my entire person, even with my boots!"
All other commandments do not relate to the entire body. We study with our eyes, mouth, and brain, eat matzah with our mouths, listen to the shofar with our ears, and wear the tefillin on the arm and head. When we enter the succah, however, our whole body is enclosed within the mitzvah and, as Rabbi Bunim pointed out, nothing that is attached to us is excluded from the mitzvah, not even one's boots.
Whereas total immersion into a mitzvah occurs physically only with succah, the concept of total involvement should extend to all other mitzvos. Just as King David says of prayer, All my bones declare, "O, God, who is like unto You?" (Psalms 35:10), so with all mitzvos, the intensity of performance should engulf one's whole personality. Indeed, one should feel that not only one's person, but everything that one has is devoted to the Divine will.
The Kabbalists state that in addition to its manifest meaning, "something we have been commanded to do or not to do," the word mitzvah also means "joined," for one attaches oneself to God by performing His will. Contact with God should not be partial. When we relate to Him, we should do so with the totality of our being. In this way, succah teaches us how to perform all six hundred thirteen mitzvos.