The Collaborative International Dictionary of English v.0.48:

Errand \Er"rand\, n. [OE. erende, erande, message, business, AS.
   [ae]rende, [ae]rend; akin to OS. arundi, OHG. arunti, Icel.
   eyrendi, ["o]rendi, erendi, Sw. [aum]rende, Dan. [ae]rende;
   perh. akin to AS. earu swift, Icel. ["o]rr, and to L. oriri
   to rise, E. orient.]
   A special business intrusted to a messenger; something to be
   told or done by one sent somewhere for the purpose; often, a
   verbal message; a commission; as, the servant was sent on an
   errand; to do an errand. Also, one's purpose in going
   anywhere.
   [1913 Webster]

         I have a secret errand to thee, O king.  --Judg. iii.
                                                  19.
   [1913 Webster]

         I will not eat till I have told mine errand. --Gen.
                                                  xxiv. 33.
   [1913 Webster]

   2. Any specific task, usually of a routine nature, requiring
      some form of travel, usually locally. An errand is often
      on behalf of someone else, but sometimes for one's own
      purposes.
      [PJC]

   3. A mission.
      [PJC]

   To run an errand, To perform an errand[2].
      [PJC]