The Kedushah, the third berakhah of the Amidah, comes in several forms in and out of the Amidah, but always has “kadosh, kadosh, kadosh Adonai tzeva’ot…” and “barukh kavod Adonai…” These lines quote Isaiah and Ezekiel, respectively.
Tzeva’ot is often translated as “hosts,” and literally means “armies.” It also may refer to those who “serve” in any way, for instance the Levites who served in the Temple. One may, of course, picture hosts of angelic creatures swirling about God and attending the Holy Presence. Angels in their hierarchy remind us that reaching higher and higher toward complete holiness is a righteous and rightful goal.
Thus many believe that lifting of the heels (and the looking upward - some with closed eyes - as another tradition) is meant as an indication of reaching higher and higher toward holiness.
Others feel it is a reaching toward communication with God, which both Isaiah (literally) and Ezekiel (in thoughts) were said to have achieved.
Some versions of the Kedushah mention specifically the ofanim and the serafim swirling in deafening sound proclaiming their praise of God. (I hope to write about angels, one week to come.) That we are standing there with our feet together (as prescribed for the Amidah) and singing like the angels described by Ezekiel, makes our lifting seem an effort to join the angels.
By the way, Catholics, Greek and Syriac Orthodox, and others recognize “kadosh, kadosh, kadosh” from their liturgy as well (in the Latin Mass it is “sanctus, sanctus, sanctus”).
The story has it that writer L. Frank Baum was visiting a synagogue with a Jewish friend, and was so taken by the lifting of the heels that he put it into one of his stories. Click your heels three times, Dorothy….