The different parts to the lulav are the palm branch, willow twigs, myrtle twigs and etrog (citron, related to a lemon). We shake them In different direction. We shake it to the north, east, south, west , up and down it shows that G-D is everywhere. This mitzvah (commandment) comes from LEV.23 : 40.
The sukkah is a hut with a thatched roof which must have at least 3 sides. It reminds us of when the Israelites had only simple shelters in the wilderness. This mitzvah (commandment) comes from LEV.23 : 42 & 43. You can find out more about the Festival of Sukkot on the My Jewish Learning website.
Daniel Eppel (5thYear)