When Abraham (then called Abram) defeated a group of armies that had conquered Sodom, and had taken his nephew Lot captive, the king of Sodom offered to Abraham all the recovered property as his reward. Abraham replied: "Not a thread nor a shoe-strap, nor shall I take anything that is yours; lest you say: 'It was I who made Abram rich.'" G‑d had promised to make Abraham wealthy, and Abraham did not want the king of Sodom to take the credit for this blessing which would come from G‑d.
The Talmud tells us that "as a reward for Abraham's statement, 'Not a thread nor a shoe-strap,' his children merited two mitzvot: the thread of blue [in the tzitzit] and the strap of the tefillin."
Our sages taught that our three Patriarchs instituted the three daily prayers; Abraham was the first to pray Shacharit (morning prayers), Isaac established Mincha (afternoon prayers), and Jacob originated the practice of Arvit (evening prayers).
This is one of the reasons why the tallit is worn exclusively during the morning prayers. Since we were given the mitzvah of tzitzit in Abraham's merit, we wear the tallit specifically for "his" prayer--Shacharit.
Visit our Tallit and Tzitzit section for more information regarding the Tallit and its associated customs.