The Shulchan Aruch (Orach Chayim 123) writes that when one completes the Amida, just before he recites "Oseh Shalom Bi'mromav…," he should bow and step back three steps. (For the details concerning how precisely these steps should be taken, see the Daily Halacha entitled "Taking Three Steps Back and Bowing: the End of the Amida," dated January 26, 2005.) What is the reason for taking three backward steps upon completing the Amida?
The Shulchan Aruch mentions perhaps the simplest and most obvious reason, namely, that upon completing the Amida we leave the presence of God as a servant humbly takes leave of his master. It would be improper for a servant to simply turn around and leave with his back towards his master. He rather steps back slowly while still facing his master, as an expression of humble submission. Indeed, the Gemara in Masechet Yoma, Daf 53A, tells of a number of Rabbis who, when leaving the presence of their teachers, would walk backwards, facing the teacher, until the teacher was out of sight. Similarly, rather than simply turning around after completing the Amida, we take leave of the Almighty by slowly stepping backward.
The Beit Yosef (commentary to the Tur by Rabbi Yosef Karo, author of the Shulchan Aruch) mentions an additional reason for stepping backwards three times. Our prayers serve as a substitute for the sacrificial service performed by the Kohanim in the Beit Ha'mikdash. After the Kohen would place the limbs and fats of the daily Tamid offering on the altar, he would walk down backwards along the ramp of the altar, which ended with three steps leading to the ground. As our prayer service corresponds to the daily Tamid offering, we end our Amida in similar fashion to the Kohen's conclusion of the Tamid ritual, and we, too, take three steps back upon concluding the Amida prayer.
Others (Orhot Hayim, Helek 1:27) explain this practice as intended to commemorate the event of Matan Torah (the Giving of the Torah), when, as the Sages tell us, Benei Yisrael fell backward a distance of three Mil (a distance roughly equal to a mile) upon hearing the frightening sound of God's voice. As we take leave of God's presence upon concluding the Amida, we commemorate the sense of awe and dread Benei Yisrael experienced when they heard God proclaim "I am the Lord your God" at Mount Sinai.
Finally, the Mechilta (Midrashic work on the Book of Shemot) in Parashat Yitro comments that after Moshe received the Torah and he descended from the top of Mount Sinai, he had to depart three heavenly "zones," referred to as "Choshech," "Anan" and "Arafel" ("darkness," "cloud" and "mist"). We commemorate Moshe's descent from these three regions by taking three steps back as we take leave of God's presence after reciting the Amida prayer.
In light of this discussion, we more clearly understand the practice mentioned by the Rama (Rabbi Moshe Isserlis, Cracow, 1525-1572), in his glosses to the Shulchan Aruch. The Rama records the custom to recite after the Amida a prayer for the rebuilding of the Beit Ha'mikdash ("She'yibaneh Beit Ha'mikdash…") and asking "make our share in Your Torah ("Ve'tein Chelkenu Be'Toratach"). Although some Siddurim omit this brief prayer, it should be recited after one takes his three steps upon concluding the Amida. As we have seen, these three steps commemorate the service in the Temple, and the events surrounding Matan Torah. We therefore beseech God and ask that He grant us the privilege of actually offering sacrifices in the Temple, rather than merely commemorating those sacrifices through the prayer service, and we ask that we earn our share in Torah as we relive our nation's acceptance of the Torah at Mount Sinai.
In the merit of this prayer, we hope and pray that God will restore the Beit Ha'mikdash to its site in Jerusalem, speedily and in our days, Amen.