The Collaborative International Dictionary of English v.0.48:

do-si-do \do`-si`-do"\, n. [from dos-[`a]-dos, back to back.]
   a movement in square-dancing in which two dancers move around
   each other in a back-to-back position, and return to their
   original places.
   [PJC]

WordNet (r) 3.0 (2006):

do-si-do
    n 1: a square-dance figure; two dancers approach each other and
         circle back to back before returning to their original
         places