What is the connection between the succah and the messianic era?
In the prophets as well as the Kabbalistic sources, we find that sukkot has a special relationship with the messianic era and a unique connection to the nations of the world.
As the spiritual climax of the year, sukkot is full of deep allusions to the messianic era - the spiritual climax of world history.
The ceremonies of sukkot clearly show the theme of redemption.
Pesach reminds us of creation - festival of Israels national creation, celebrated in spring (rebirth).
Shavuot commemorates Revelation of Hashem at Sinai, we celebrate with all night study.
Sukkot however, looks ahead to the final redemption. In the hoshannot we call out to Hashem to "please save us" (hoshiana na) The arba minim symbolising all the people of Israel joined together as one united group, hinting to the future.
Another allusion to the connection between sukkot and the mesianic era can be found in the haftarah for sukkot which describes the prophecy of the war of Gog and Magog.
The next source shows the connection between the sukkah and the battle of Gog and Magog.
Rabbi Shimson Raphael Hirsch discusses the connection.
In the name Gog we see the word Gag, roof, something sturdy which has been built to protect us as opposed to the Sukkah which has a very weak roof made of twigs and branches.
Just as people have the power to make themselves safe and secure by building strong roofs, so they delude themselves into thinking they can make themselves safe from that which comes from above, namely Hashem . They think they can find security in the protection of their own might.
The battle of Gog and Magog is a battle of the Roof agaisnt the sukkah, the illusion of human strength and power against the sukkah truth of the confidence in Hashems protection.
Unlike all other festivals, the Temple offerings of Sukkot are dedicated to the nations of the world.
The Netziv explains that in the Days to come, the nations of the world will bring offerings to Jerusalem on Sukkot as we read in Zecharia ch. 14, in the full knowledge that their own well-being depends on the Temple.
Another prophecy of Yeshaya describes how foreign nations will come to Jerusalem to guard the people of Israel.
Because the ultimate destiny of the world also includes the foreign nations, on Sukkot, the festival of destiny, we pray even for these seventy primary nations to reach their purpose.