Source : Webster's Revised Unabridged Dictionary (1913)

Undertake \Un`der*take"\, v. t. [imp. {Undertook}; p. p.
   {Undertaken}; p. pr. & vb. n. {Undertaking}.] [Under + take.]
   1. To take upon one's self; to engage in; to enter upon; to
      take in hand; to begin to perform; to set about; to
      attempt.

            To second, or oppose, or undertake The perilous
            attempt.                              --Milton.

   2. Specifically, to take upon one's self solemnly or
      expressly; to lay one's self under obligation, or to enter
      into stipulations, to perform or to execute; to covenant;
      to contract.

            I 'll undertake to land them on our coast. --Shak.

   3. Hence, to guarantee; to promise; to affirm.

            And he was not right fat, I undertake. --Dryden.

            And those two counties I will undertake Your grace
            shall well and quietly enjoiy.        --Shak.

            I dare undertake they will not lose their labor.
                                                  --Woodward.

   4. To assume, as a character. [Obs.] --Shak.

   5. To engage with; to attack. [Obs.]

            It is not fit your lordship should undertake every
            companion that you give offense to.   --Shak.

   6. To have knowledge of; to hear. [Obs.] --Spenser.

   7. To take or have the charge of. [Obs.] ``Who undertakes you
      to your end.'' --Shak.

            Keep well those that ye undertake.    --Chaucer.

Undertaking \Un`der*tak"ing\, n.
   1. The act of one who undertakes, or engages in, any project
      or business. --Hakluyt.

   2. That which is undertaken; any business, work, or project
      which a person engages in, or attempts to perform; an
      enterprise.

   3. Specifically, the business of an undertaker, or the
      management of funerals.

   4. A promise or pledge; a guarantee. --A. Trollope.

Source : WordNet®

undertaking
     n 1: any piece of work that is undertaken or attempted; "he
          prepared for great undertakings" [syn: {project}, {task},
           {labor}]
     2: the trade of a funeral director