Why did the Rabbi hand me a kerchief?

Question: Why does the Rabbi who sells the chametz before Pesach ask me to lift a sudar (kerchief) or something equivalent when I submit my chametz form?

Also, if this practice is indeed required, is the sale of chametz valid if this was omitted?

Answer: The Shulchan Aruch (Choshen Mishpat 182:1) states that when appointing a shliach (emissary) to acquire or sell something on one's behalf one does not need to perform any kinyan at all; simply requesting of the person to do so appoints them as the shliach:

ואין העושה שליח צריך קנין ולא עדים, אלא באמירה בעלמא בינו לבין חבירו 

שולחן ערוך חושן משפט הלכות שלוחין סימן קפב סעיף א 

Therefore, an appointment can be made verbally, over the telephone, by mail, etc. and the deed is perfectly valid.

However, it is customary to reinforce the appointment through the process of kinyan sudar. This is similar to the practices referred to by the Rambam (Hilchos Mechirah 5:11-13) that are of no consequence at all but are merely done to demonstrate that the parties involved are serious about what they are doing.

But, there is another aspect to the sale of chametz that indeed requires this form of kinyan -- not between the Rabbi and the Jew who appoints him as his agent -- but between the Rabbi and the nochri.

There are many kinds of kinyanim (modes of acquisition) that serve to acquire an object, but not all work in every circumstance. Therefore it is customary to employ all the various forms of kinyan when selling the chametz to the goy, just to be sure that it is indeed sold. Kinyan Sudar is therefore used as well when the Rabbi sells the chametz to the nochri.