A turban (from Persian دولبند, dulband; via Middle French turbant) is a type of headwear based on cloth winding. Featuring many variations, it is worn as customary headwear by people of various cultures. Communities with prominent turban-wearing traditions can be found in the Indian subcontinent, Southeast Asia, the Arabian Peninsula, the Middle East, Central Asia, North Africa and the Horn of Africa.
Wearing a turban (Amama) and Aba Qaba (Religious Robe) is recommended during performing Salah (Prayers). Wearing Amama in public now a days can mislead people that the person is a scholar then his behavior can be taken by lay people as a religious behavior, that is why it should be avoided unless the person is really a religious scholar or religious student.
The black turban is the turban of the Prophet Muhammad (SAWA). This fact is mentioned in both Shia and Sunni books.
The Sayyed Ulama wear black turban which is the turban of their great grand father, the Prophet Muhammad (SAWA).
Yes, there is a Hadeeth is Makarimul Akhlaaq (Page 119) from the Prophet Muhammad (SAWA) that : Praying with turban is much more better than praying with out turban.