The most powerful tribe of the Anatolian Turks were the Osmanis, from which the name Ottoman was derived. The Osmanis were able to break away from the domination of other Turkish rulers, the Seljuks, in 1281. They were able to establish a dynasty which would rule large territories in the Middle East (and beyond) for over seven hundred years. A large amount of their mystique came from a legend about the first Ottoman, Osman. Legend goes that he was the subject of a prophetic dream while he served as a warrior (against the Seljuks) in 1281.
Osman had all the qualities of an excellent fighter, he had loyalty to his tribe and good skills as a horseman. He wished to marry a woman who had fallen in love with, the daughter of an important local Shaykh (holy man). Despite all this, the Shaykh refused to let his daughter to marry Osman, because he didn't think the young soldier had much of a future. That night, however, the Shaykh dreamed that his daughter became one with a vibrant full moon, and that a large tree grew out of her chest, covering the entire world with its shade. He took it as a sign that Osman did have a great future, and the next day he gave his approval to the union. This legend about his vision, along with a (claimed and most likely false) genealogical tie with the Prophet Muhammad, gave the Ottomans a legitimacy which they used to assert their authority over other rivals struggling to rule Anatolia.
Lecture from various classes at University of Central Florida, and my own memory