Succot is the longest of the Sheloshah Regalim (Pilgrim Festivals), each of which is based on historical events on the one hand and on the agricultural season on the other. The two Mitzvot specifically connected with Succot, of the succah and arba'ah minim, illustrate this concept.

The succah (shelter) is a reminder of the history of the People of Israel and specifically, of the Exodus from Egypt.

So that your future generations should be aware that I housed the Israelites in shelters when I brought them out of Egypt.
Leviticus 23:43

The arba'ah minim (four species of plant) suggest nature and the national land as a reminder to the settlement of the land.

On the first day you shall take the fruit of… and rejoice before the Lord your G-d for seven days.
Leviticus 23:40

The succah effects the concept of Hashgachah - personal (Divine) supervision. G-d rules the world and supervises it.

On a day of trouble, He will hide me in his shelter!
Psalm 27:5

All the stormy winds in the world cannot destroy the shelter of Divine protection, because Israel trusts in G-d.

This personal supervision obliges Israel to be united:

Who in the world is a single nation like your people Israel?

The great joy we are commanded to have in a special way on Succot expresses submission to G-d, from a feeling of recognition of G-d's favours and from gratitude: that He brought us out of Egypt, and concerned Himself about all our needs during forty years of wandering in the desert. We are therefore extremely happy and grateful to G-d for all His good, on behalf of our our forefathers and ourselves.