Kedusha: V'kara Zeh El Zeh V'amar
This mysterious and ambiguous practice is actually without any authentic source at all. In fact, there is no evidence of any great rabbis in earlier generations ever doing so. Nevertheless, the practice has become so widespread in recent times that a number of interpretations have been offered to rationalize it.
It is written in the siddur "Tefila L'david" of the Lelover Chassidim that when one recites “V'kara Zeh El Zeh V'amar" one should bow to the right and then to the left as if one is soliciting authorization to praise God.  One will note that the opening line of the Kedusha is a declaration of our desire to praise God just like the angels do so in Heaven. Since the angels stand on either side of God, bowing to the right and left is intended to symbolize that we are humbly requesting their permission to praise God as they do.
Similarly, it is also suggested that bowing to the right and left is intended to symbolize the entire congregation turning to one another in order to praise God in unison, just as the angels do. This emphasizes the vital aspect of achdut, unity, during prayer – a unity characteristic of the angels. Indeed, there was once a custom, now extinct, not to bow right and left at "V'kara Zeh El Zeh V’amar," but rather, to wave one's hands towards others in one's proximity. This too, symbolized uniting the congregation and ensuring that everyone was ready to recite the Kedusha together in unison.
Some commentators suggest that bowing to the right and left is intended to recall that God is praised from all sides by the Heavenly hosts. It may also have been a custom created in order to arouse a feeling of humility before reciting the angelic praises, and in fact, a form of requesting permission from God Himself to do so. There is also a theory, based on the Zohar, that bowing to the right and left is intended to recall the rainbow and the story of Noach.It is worth noting that bowing from side to side is also practiced elsewhere, such as Birkat Kohanim, Oseh Shalom in Kaddish, Oseh Shalom at the end of Shemoneh Esrei, and Bo'i Kallah in Lecha Dodi.
Other sources seem to point to the liturgical song of "Amitzei Shechakim", recited on Yom Kippur, as the source for the custom to bow at Kedusha. The "Amitzei Shechakim" prayer mentions the angels turning to "every side" when reciting the Kedusha praises. In any event, it appears from all sources that bowing at "V'kara Zeh El Zeh V'amar" is related to the angels in one way or another. It is also taught that when the angels recite kedusha they also bow somewhat: they turn towards the north, east, and west.
One of the reasons we rise upon our toes each time we say the word “kadosh” is in order to symbolize that God’s Holiness, and all of that which is in Heaven, is on a higher level of holiness than that which exists in this world. Hence, rising upon our toes symbolizes our desire to reach this higher level of holiness. One should also look upwards when reciting “kadosh, kadosh, kadosh”.
In addition to the custom of turning to the right, left, and center at the words "V'kara Zeh El Zeh V’amar", there was once a custom, based on the teachings of the Arizal, to do so each time one said the words "Kadosh" in Kedusha. The Arizal taught that each "Kadosh" in “Kadosh, Kadosh, Kadosh” represents a different intellectual attribute. The first “kadosh” represents the attribute of kindness elevated by wisdom, which emanates from the right side. The second “kadosh” represents the attribute of strength elevated by understanding, which emanates from the left side. The third “kadosh” represents the attribute of beauty elevated by knowledge, which emanates from the center. Our desire to experience these mystical manifestations is also one of the reasons that we rise on our toes when saying "Kadosh, Kadosh, Kadosh." Some people have the custom to rise a little higher each time “Kadosh” is recited while other sources indicate that there is no need to do so. There is also a custom to rise on one’s toes only once in the course of “kadosh, kadosh, kadosh”.
Although most individuals begin the "V'kara Zeh El Zeh V'amar" movements with the right side, there is no real reason to prefer one side over the other. Nevertheless, there is a general rule that the right side is to be given preference whenever possible.  This is based on the verse in Tehillim that says "God's right hand is mighty!” Indeed, we wash our right hand first, put our right shoe on first, and always hold objects that are being used for a mitzva with our right hand, to name but a few examples. This is likely why common custom is to first bow to the right in “V’kara Zeh El Zeh V’amar.” There was once a custom to bow each time God’s name is mentioned in the Kedusha passages of “Baruch Kevod” and “Yimloch” though this is no longer practiced today.
In some communities, it is customary for only the chazzan, not the congregation, to recite the opening line of Kedusha (“Nekadesh” or “Nakdishach” depending on nusach) as was the original custom. According to this approach, the opening line of Kedusha is specifically for the one leading the service, in which he seeks permission on behalf of the congregation to praise God with the Kedusha prayer. In most Ashkenazi communities, however, everyone recites the opening line of Kedusha. Those who follow the teachings and practices of the Arizal recite the “intermediary” verses of Kedusha, as well. On Shabbat and Yom Tov it is almost universal custom for everyone to recite all of kedusha responsively with the chazzan.
 Az Nidberu 13:32:3.
 Cited in Minhag Yisrael Torah, OC 125:2.
 Yeshayahu 6:3; Shivat Tzion Vol. 2 p.117.
 Kaf Hachaim (Rav Palagi) 15:1; Ben Ish Chai, Beshalach.
 Parshat Noach, cited in Minhag Yisrael Torah, OC 125:2.
 Cited in Minhag Yisrael Torah, OC 125:2.
 Zohar, Noach, p.71b, cited in Otzar Teshuvot (Klein) 83. See there for more.
 Netivot Olam, Netiv 11 cited in Rivevot V’yovlot 3:66.
 Rema, OC 125:2.
 Minhag Yisrael Torah O.C. 125:2.
 Rivevot V'yovlot 3:66. See also Sefer Kushiot 173 and 163.
 Kaf Hachaim (Palagi) 15:60.
 Aruch Hashulchan, OC 125:3; Rivevot Ephraim 5:75:1.
 Az Nidberu 13:32.
 Sota 15b, Zevachim 62b, Minhag Yisrael Torah 134:1.
 Tehillim 118:15. See also Vayikra 8:23-24.
 Mishna Berura 125:2.
 Tosefta, Berachot 1:11; OC 125:1; Mishna Berura 125:1; Az Nidberu 13:32. See also Teshuvat Harosh 4:19; Tur, OC 125.
 Taz, OC 125:1; Mishna Berura 125:2; Aruch Hashulchan, OC 125:1,2. See also at length Shorshei Minhagei Ashkenaz Vol. 1 p.23-45.
 Rav Chaim Vital, Shaar Hakavanot.