We refer to the succah as "succath shalom", the succah of peace. How is the succah connected to peace?
When we leave our houses, and enter the succah, we are going to a less material, more spiritual place. A house is a stable material building, while the succah is an unstable construct. Of course, it is still material (you can touch it), but because of its instability it is less connected to the material world, and our reason to eat (and in warm places to sleep) there is purely spiritual (the Torah commends). So we are moving away from materiality, and approaching the spirituality.
Materiality is a world of fights. The resourses are constant. When I give something to you, I have less, you have more, when I take, then you have less and I have more (using game theory terms it is a sum-zero, or win-loose situation). Spirituality is a world of cooperation, since one cannot loose. If you teach me something, I have more, but you don't have less. In fact you'll have more too, since teaching is a very effective form of reviewing. We both end up having more (Win-win sitation)
In a world, where there are only win-win situations, there is no reason to fight. That's why Succah represents peace. It symbolizes a reality where only win-win situations exist.
