My Chabad rabbi always puts on a black sash before praying. We joke that it is because he has attained a "black belt" in prayer arts. But seriously, what is the meaning of that sash?
The black belt you refer to is called a gartel in Yiddish (similar to the English word "girdle").
There are a number of significances associated with the gartel. Allow me to share them:
A. Jewish law mandates that the "heart does not see the nakedness" when one recites the Shema and other prayers. This means that the upper body (more specifically the heart) be separated from the lower half, which has a coarser function. In ancient times, when common clothing consisted of a simple, loose robe, it was necessary to tie a belt around one's waist to insure that the nether region was out of view of the heart.
B. We read in Amos, "Prepare yourself toward the L‑rd your G‑d." Our sages infer from here that one must dress himself up before facing his Maker in prayer. Part of this preparation is to gird oneself with a special belt. Hence the custom of wearing the gartel even though modern clothing ensures that that the "heart does not see the nakedness."
C. The gartel is reminiscent of the belt which the priests would wear during their service in the Holy Temple in Jerusalem. It is for this reason that many are particular to wear their gartel at elbow height, just as the priests of old did.