One of the major themes of Hakhel is the unity of the Jewish people. Hakhel was a re-experiencing and recommitment to Matan Torah. At Har Sinai, the Jewish people were also in a state of absolute unity. So too at Hakhel, there had to be a gathering of all of Klal Yisroel together.
During the Hakhel year, we have to strengthen our Ahavas Yisroel. For this reason, the Rebbe would hold the Esrog together with the Lulav for the entire Hallel (which is not the usual Chabad custom) as an act of personal Mesiras Nefesh for Achdus during Hakhel.
The Parsha also contains the Mitzvah of fearing (revering) the Mikdash. This refers to how one must conduct themselves in a respectful manner when entering the Beis Hamikdash. The commentators explain that Hakhel took place in the Beis Hamikdash as the holiness of the place would cast awe on the people. The fear of Hashem was one of the key objectives of the Hakhel gathering.