The holiday of Succot has many attributes that combine to a unique and special occasion. These special attributes are created by the mitzvot that are performed during the holiday, and in the various ways that Succot is referred to.
There are many mitzvot that are specific to Succot. Aside from living in the Sukkah and the Arba Minim, there are also those that relate to the Beit Hamikdash such as the 07 korbanot of the Musaf sacrifices, the Nisuch Hamayim, pouring the water on the Mizbeach, followed by the Simchat Beit Hashoeva. Succot also has many names. In davening we call it Chag HaSuccot and Zman Simchatenu. In the Gemarah it is simply called Chag, and also Chag Ha'Asif, the Harvest Festival. All the above ideas combine to create Succot.
In Pirkei Avot ד:א() states איזהו עשיר? השמח בחלקו. "Who is rich? One who is "Sameach" with his share. It seems that rabbinically, "Sameach" is contentment or satisfaction not just joy or happiness. Simcha is actually a state of mind. We say in davening ישמחו השמים ותגל הארץ, The land and the heavens are happy. Simcha associates with Heaven while Gilah associates with Earth. Simcha is a word that is reserved for the heavens and Gilah is used regarding the mortal Earth even though both these words have the same meaning.
Using this idea we can begin to understand how a few references from above relate to the holiday of Succot more deeply. Succot is referred to as Zman Simchatenu, a time to feel simcha, contentment with our share. During Succot Hashem shows us that we must be content with what we have, for this is what He has given us. To show Hashem that we believe Him that all we have is His doing, we put ourselves in Hashem's hands for 8 days. Thus Succot is referred to simply as Chag because this is the holiday where we are truly Sameach and show that we are truly content with what we have.
Succot is also referred to as Chag Ha'Asif. Succot was placed right before the harsh winter season and we thank Hashem for giving us enough food to survive this rough season. Therefore Succot is placed before the winter when we feel a great need for spiritual help through the rough times ahead.
Now lets look at the Simchat Beit Hashoeva. Rav S. R. Hirsch, in his commentary on Chumash, describes Nissuch Hamayim as "pouring every drop of the person's joy in life into the foundations of the Mizbeach of Hashem, signifying that joy as coming from Hashem." Again we see the connection to simcha, happiness in the portion that Hashem has given to us.
In regard to the 07 Musaf korbanot that were brought during Succot and Shmini Atzeret, these correspond to the 07 nations of the world. We see here a very different message from other Yamim Tovim. Here Hashem is the provider for the entire world; we don't just celebrate the fact that Hashem helps us alone. It says in Tehillim 541:61, פותח את ידך ומשביע לכל חי רצון - You open your hand and feed every living thing what it desires. In contrast to such chagim as Pesach and Shavuot, Divine aid and sustenance is a universal theme and the entire world must be thankful for that.
During this holiday of Succot we should all remember to be good and rejoice with what we have. If we were all satisfied with what we have the world would be a much better place.