Tasawwuf is a branch of Islamic knowledge which focuses on the spiritual development of the Muslim.
Allah sent His final messenger, Prophet Muhammad , as a source of knowledge for the entire ummah. He was the fountain of Quran, Hadith, tafsir, rhetoric, fiqh, and so on. After the Prophet, the scholars of this ummah carried and propagated each of these branches of knowledge. Because no one person can attain the perfection of the Prophet , who single handedly assumed all of these roles, various branches of the Islamic sciences developed. For example, Imam Abu Hanifah preserved the science of fiqh and after him thousands of scholars continued in his footsteps. Hence these scholars preserved the fiqh of the Prophet . Similarly Imam Bukhari and the other famous scholars of Hadith, preserved the words of the Prophet. The scholars of tajweed preserved the recitation of the Prophet . And, the scholars of Arabic grammar preserved the language of the Prophet .
Along these lines, the Prophet was the model of spirituality for the world. His God-consciousness, deep spirituality, acts of worship, and love for Allah were preserved and propagated by an Islamic science called Tasawwuf. The aim of the scholars of this science was purification of the heart, and development of consciousness of Allah through submission to the shariah and sunnah.
Studying the life of the Prophet , the scholars who propagated the science of tasawwuf understood that a requisite for approaching Allah was abandonment of the common pursuits of the world. They often wore wool because of its simplicity and low cost. In Arabic the word for wool is suf and thus, those who wore it became known as the Sufis. Another possible derivation of the word comes from the root wordsafa, which means "to clean." Because the scholars of tasawwuf focused on cleansing the heart, they later became known as the Sufis.