The "heavens" and the "earth" in our lives are Torah and mitzvos. Torah is checking in with heavenly truth and mitzvos is applying that here on earth. When Moshiach comes, the world will be completely refined and we will be close to the earth in the most ideal way. (Based on Likkutei Sichos Vol. 9, pp. 204-214.)
We sit in the sukkah to commemorate the clouds that Hashem protected us with when we left Egypt. What does the High Holiday season have to do with clouds? Water, representing our physicality, evaporates in the sunlight of spirituality until it becomes a refined mist. Then we start the cycle all over again on a higher level with the Prayer for Rain on Shemini Atzeres. (Based on 4th Night of Sukkos 5750 in Hisva'aduyos 5750 vol. 1 pp. 163-4.)
The victory over all external enemies in the time of Moshiach will reflect the victory over all internal challenges achieved through the process of self-refinement culminated on Sukkos. (Based on sichos of Sukkos 5724 in Sichos Kodesh pp. 13-14.)
Our Sages tell us that Torah begins and ends with kindness. What do these two acts of kindness teach us about when to turn to Hashem for kindness? And what parallel does this have with our journey through the High Holiday season? (Based on Igros Kodesh, vol. 2, Letter #169.)
How the first three verses of Torah may be read as the story of each of our lives. (Based on an article from HaKria V'HaKedusha.) In observance of the 2nd yahrzeit of R' Shneur Hirsch a"h.
From the fact that Noah looked for signs that the flood was over we learn the importance of looking for signs of Moshiach's arrival. (Based on a sicha from 10 Tammuz 5745.)
There is no real contradiction between personal growth and being an activist who helps others. The way that we discover our inner talents is by going out into the world and dealing with other people. (Based on Sefer HaSichos 5749 p. 47.)
Part of the impact that a mitzvah has on the world is related to the physical effort that it requires us to expend. Avraham's healing process after his circumcision was thus essential to his bris milah having the fullest possible effect. (Based on Likkutei Sichos Vol. 5, p. 82.)
When Yakov received the blessings from his father Yitzchak he was dressed like his wicked brother Eisav. Why was it important to be blessed while wearing such a costume?