The Rambam writes that at Hakhel, the people would listen to the words of the Torah with awe… like on the day the Torah was given at Har Sinai. Hakhel was a reexperiencing of the covenant at Sinai.
In addition to hearing the words of Torah, one of the messages of Hakhel is the gathering and unity of the Jewish people.
The Jewish people arrived in Midbar Sinai on Rosh Chodesh Sivan. Based on the use of the word ויחן in singular form, the sages teach that they camped at Sinai in absolute unity; like one man with one heart.
Chassidus explains that the key to achieving unity is humility. The trait of humility is represented by Har Sinai, which was chosen by Hashem because it was the smallest mountain.
The desert also represents the quality of humility. The desert is a place that is Hefker, which no one owns and the lowly dust of the desert is trampled and tread upon by all.
The oneness and unity of Midbar Sinai was also experienced at Hakhel.