Q. Why do Jewish men were a Tallit when they pray?
The Torah commands us to wear Tzitzit on all four-cornered-garments that we wear during daylight hours (Numbers 15:38). The paragraph in the Torah that includes this command is read every morning as the third paragraph of the Shema prayer.
Tzitzit are wool strings that are tied to each of the four corners of the garmnet. According to Jewish tradition the Tzitzit are made of eight white strings on each corner tied with five knots. While there is no command to wear Tzitzit if one is not wearing a four-cornered-garment, Jewish men have always worn four cornered garments so they can fulfill the mitzvah of wearing Tzitzit.
According to Kabbalah being wrapped in a four-cornered-shawl with Tzitzit on it while praying, arouses G‑d's mercy. For this reason Jewish men wear a four-cornered-shawl or Tallit during the morning prayers and on Yom Kippur.
The Torah exempts women from most commandments that are limited to certain times. Since the Tzitzit need only be worn during the day, women are not obligated to wear them. Although, Jewish women may also fulfill Mitzvot that they are exempt from, they may not wear a Tallit since it the Torah forbids cross dressing (Deuteronomy 22:5) and the Tallit has always been a male garment.