See Shulchan Aruch, Orach Chaim 48, Rema and Mishna Brura there. Some say shokeling is in order to arouse one’s energy.
Why do Jews shokel, move back and forth when davening and learning?
The Zohar says the reason Jewish people shokel is because we are hewn from the holy lamp as it says נר ה' נשמת אדם, a man’s soul is the lamp of Hashem. Once this lamp has been kindled from the supernal Torah the light upon it never ceases for a moment, like the flame of a wick which is never still for an instant. When a Jew has said one word of Torah, a light is kindled and he cannot keep still but sways to and fro like the flame of a wick.
Another reason for shokeling is told to us by the Baal Haturim. On the pasuk which it says at Har Sinai, וירא העם וינעו, the nation saw and trembled, the Baal Haturim tells us that the reason for swaying back and forth while learning Torah is because the Torah was given with awe, trembling and quaking.
In the Sefer Kuzari, the Rabbi reveals to the Kuzari an astounding reason as to why we shokel: it is because there would be ten or more people gathered around to read one sefer. This is why many of the sefarim back then were large. Because the sefarim would rest on the ground, each of the ten would have to regularly bend over to read a word and then stand erect afterwards to allow another to bend over and read. This is how moving back and forth originated. From that point onward it became an accepted tradition because people looked at the movements of others and wanted to emulate them, which is human nature.
