The holy Zohar refers to the Sukkah as צלא דמהימנותא - the shade of faith. On three separate occasions the Torah commands us to rejoice on Sukkoth. Is there any connection between what a Succah represents and the commandment to rejoice on Succoth?
King Solomon in his wisdom, explains to us that Simha (joy), is meaningful only when it is associated with our purpose in this world: attaching ourselves to Hashem, through the performance of the Miswoth (commandments), (Qoheleth 8).
We may experience temporary feelings of happiness when we buy a new outfit, or when we eat delicious dessert, etc. but the everlasting emotion of Simha, true happiness, is possible only when we attach ourselves to our Creator, the Source of all good.
The Sukkah is the shade of our faith in the Holy One blessed be He. Without faith, our lives are dull and meaningless. Always, but especially on Sukkoth, when we are commanded to rejoice, we make a statement that having faith in the One who protects us creates a deep and most meaningful joy within us.
Rabbenu the Arizal points out that the two walls and part of a wall which is the minimum requirement for a Sukkah to be Kasher, alludes to G-d's "arms" hugging us. We can all relate to a loving arm hugging us constantly.
How much more so the "loving arm" of our Father in Heaven! Rejoice and be happy!