Torah requires Jews to wear a garment of some type to cover themselves, while praying, and such garment must have fringes (tzitzit) attached to its 4 corners. The covering of oneself in the Tallit, during the prayer, is seen as a symbolic covering of oneself with the presence of God and separation from the natural world around.
The custom of wearing Tallit dates back to 1800 BC, although the form of the tallit has changed throughout time and the form known to us today was adopted around 1000 CE.
It is common for both men and women to wear a tallit, it is worn over the outer clothes during the morning prayers on weekdays, Shabbat and holidays. The tallit is traditionally draped over the shoulders, but some cover their head with it.
Traditionally, Tallitot are given to children on their Bar Mitzvahs or Bat Mitzvahs, as a gift by a father to a son or a mother to a daughter, but it is also common to present a tallit to a groom before marriage, as part of the dowry.
Talit also might be purchased to mark a special occasion or as a gift to a community synagogue.
Nowadays, a variety of designs of tallit are available and it became a matter of style and fashion to bring your own designed tallit to synagogue.
The Cabalists around the globe use the tallit and consider it as a special garment for the service of God, intended to inspire awe and reverence for God at prayer.