According to Leviticus 23, #sukkot must be celebrated with palm fronds, leafy tree branches, willow branches, and fruit from good trees. It also says that native Israelites are to live in temporary shelters (literally "sukkot") for seven days. Tradition says to make these shelters of tree limbs and boughs, but I think any temporary, portable shelter is sufficient as long as branches and fruit are included in the celebration somehow.
Why are sukkot often made from branches? One possible reason is because a tree can't be unclean. Ezra and Nehemiah built their sukkot from olive, myrtle, palm and other tree branches. See Nehemiah 8:15.
Trees are linked to Sukkot throughout Scripture. See Isaiah 4:2-6 and "the branch of YHWH" for example. Sukkot is one of three harvest festivals on God's calendar along with the early Unleavened Bread and Shavuot/Pentecost. See Deuteronomy 16:13.