verb

• (transitive) To designate or set apart (something) for some purpose.
  "to assign a day for trial"
• (transitive) To appoint or select (someone) for some office.
  "to assign counsel for a prisoner"
• (transitive) To allot or give (something) as a task.
  "“I cannot do it, Sir !” was his reply. “I fire into their ranks, and that does as well ; but to single out one among them, and mark him for death, would lie upon my mind afterwards.” The man who could feel thus was worthy of a better station than that in which his lot had been assigned."
• (transitive) To attribute or sort (something) into categories.

noun

• (obsolete) A thing relating or belonging to something else; an appurtenance.
  "The King ſir hath wagerd with him ſix Barbary horſes, againgſt the which hee has impaund as I take it ſix French Rapiers and Poynards, with their aſſignes, as girdle, hanger and ſo."
• (obsolete) An assignment or appointment.
• (obsolete) A design or purpose.
  "He aim’d at high designs, and so attain’d / The high assigns to which his spirit aim’d."