There are three major traditions associated with the celebration of Sukkot: building a sukkah, eating in the sukkah and waving the lulav and etrog. The lulav and etrog are actually four different kinds of plants (called the "Four Kinds" or "Four Species") that are brought together and waved while reciting blessings. They include a citron, a palm branch, three myrtle twigs and two willow branches.
But have you ever wondered why we wave the lulav and etrog? According to Rabbi Alfred Kolatch, the tradition of waving an item during worship can be traced back to Leviticus 7:34 and Leviticus 14:12. Here the act of waving is interpreted as bringing the offerer of a sacrifice closer to God, perhaps because the smoke from the burnt offering was being fanned towards the heavens. In Talmudic times, some rabbinic authorities also believed that the act of waving would shoo away evil spirits.
You can learn more about the Four Species and how to wave the lulav and etrog in these About Judaism articles:
Reference: "The Jewish Book of Why." Rabbi Alfred Kolatch. Jonathan David Publishers, Inc.: New York, 1981. pg.150.