Wikipedia
Ashraaf comes from Arabic (أشراف) and is the plural form of Sharif or Shareef (شريف), which literally means "noble" or "privileged". In some countries it used as a term to denote descendants of Muhammed (see Sharif or Shareef). Among South Asian Muslims it used as a term for the Muslim gentry in South Asia, usually claiming Arab or Turkish descent. This group is the equivalent, in some ways, of the European concept of the "gentry" and families/clans within this group have a family name that signify their position—often based on descent from The Prophet, his immediate circle, major Sufi personalities, or from Genghis Khan or other Mongol and Turkish warlords. (See Baig and Khan.) Some families also have names based on places in (both places in South Asia and places in Iran, Afghanistan and the Arab world—like Badakhshani from the Badakhshan province of Afghanistan) or Sufi orders—thus Chishti or Warsi might signify an affiliation/reverence to Moinuddeen Chishti or Nizamuddin Chishti on the one hand or the saint at Dewain Shareef on the other. In the latter case, sometimes, a person will not use the name till they have taken a formal oath of allegiance (bayth) or been initiated into the order. Also, in some cases, the name might have been originally acquired by one ancestor in one of the last couple of ways and then used as a family name.
In Somalia and Djibouti, the term is used to denote a community that is presumed to have been descended from the Prophet Muhammad.