Question:

Why does a praying person - מִתְפַּלֵּל mitpalel wear a טַלִּית tallit during prayer?

Answer: 

In the Torah it is written: Speak unto the children of Israel, and bid them that they make them throughout their generations fringes - צִיצִת tzitzit on the corners of their garments, and that they put with the fringe of each corner a thread of blue. (4M 15:38)

Since biblical times the clothing that we wear has changed, therefore we do not put the fringes directly on clothing, but we attach them on the tallit.

The tallit is a blanket of rectangular shape, made from a white material, on the corners of this covers the fringes made of white and blue threads are placed.

On the base of this commandment, the person leading the prayers, or the cleric leading the worship or other religious ceremony wears a tallit, he puts the tallit over his head.

Other worshippers put the folded tallits over their shoulders.