To shawkle means, in Yiddish, to shake. Gib a shawkle colloquially means
"Get a move on it! Shake a leg." Shawkling in a synagogue during prayer, certainly
an everyday occurrence and sight is emotional, ritual swaying.
There seems to be two general styles: forward and back swaying, usually seen in high
emotional prayers requiring intense concentration, and side to side shawkling, with the
shifting of body weight from one foot to the other, usually seen during less intense
standing prayer. There is one style of shawkling which the sources strictly forbid,
even though it is often observed; one should never twist left and right and right
and left while davening, for it may appear as if you are physically saying "no" to
G-d when you pray.
There are probably as many explanations for shawkling as there are Jews. Below are a
few of the more common ones:
Of course those who do shawkle while davening, no doubt agree with the last reason,
if you asked them they would probably give you one or two other reasons and explanations of
their own. This subject and many others can be found in a book called "The Book of Jewish
Customs" by Harvey Lutske. Regardless, whether you shawkle front and back or rock on your
feet or don't shawkle at all during davening, the important thing is that you pray with
kavanah, concentration and intent.