The first biblical reference to booths is found here:
Genesis 33:17 Jacob journeyed to Succoth, and built for himself a house and made booths for his livestock; therefore the place is named Succoth.
Moses expanded this idea into a time of celebration for Israel:
Leviticus 23:34 “Speak to the sons of Israel, saying, ‘On the fifteenth of this seventh month is the Feast of Booths for seven days to the LORD.
Booths were temporary housing which foreshadowed the church of saints first drawn to the resurrected Christ that we see in the New Testament.
It was not God’s intent that Israel live indefinitely in booths. Neither was it His intent that the New Testament church go on indefinitely. It was only to house the believing until the kingdom of God came. And that was to happen, of course, before the generation of Jesus’ contemporaries had all passed away (Matthew 10:23; 16:28; 24:34). (If you are in doubt, see Jesus Christ Has Already Come Again.)
See also these posts:
Scripture quotations taken from the NASB, unless otherwise noted.