According to the Mishnah (daf, of page 61a), the special Shavuot sacrifices – the shtei ha-lehem and the kivsei atzeret – the two loaves and the lambs brought for sacrifice – needed tenufah – waving – done to them. Tenufah is defined in the Mishnah as lifting them forwards and backwards, upwards and downwards.
Rabbi Hiyya bar Abba said in the name of Rabbi Yohanan, forward and backward,that is to Him unto Whom the four directions belong; upward and downward, that is to Him unto Whom heaven and earth belong.
In the West (in the Land of Israel)it was taught as follows: Rav Hama bar Ukva said in the name of Rabbi Yose bar Rabbi Hanina, forward and backward, in order to keep off violent winds; upward and downward, in order to keep off harmful dews.
Rabbah said, Likewise with the lulav.Rabbi Aha bar Yaakov used to swing it forward and backward, and hold it out and say, ‘An arrow in the eyes of Satan!’But it is not proper to do so, for it is a challenge to Satan to contend with him.
Rishonim point out that there is a practical difference between the reason suggested by Rabbi Hiyya bar Abba in the name of Rabbi Yohanan and the one raised by Rav Hama bar Ukva in the name of Rabbi Yose bar Rabbi Hanina. According to the first approach, the point of waving the sacrifices in different directions is in order to offer thanks to God who rules the entire world. Such recognition would be appropriate in all sacrifices. The second approach, which connects waving the sacrifices with wind and dew, would appear to be appropriate specifically at seasonal crossroads, e.g. the holiday of Shavuot when the fruits of the tree are judged and on Sukkot when judgment is made regarding rain for the upcoming season.