The Collaborative International Dictionary of English v.0.48:

committed \committed\ adj.
   1. Bound or obligated, as under a pledge to a particular
      cause, action, or attitude. Opposite of uncommitted.

   Note: [Narrower terms: bound up, involved, wrapped up;
         dedicated, devoted; pledged, sworn]
         [WordNet 1.5]

   2. Associated in an exclusive sexual relationship; also
      called attached. Opposite of unattached.

   Note: [Narrower terms: affianced, bespoken, betrothed,
         engaged, pledged, promised(predicate); married]
         [Also See: loving.]

   Syn: attached.
        [WordNet 1.5]

   3. Consigned involuntarily to custody, as in a prison or
      mental institution.
      [WordNet 1.5]

The Collaborative International Dictionary of English v.0.48:

Engaged \En*gaged"\, a.
   1. Occupied; employed; busy.
      [1913 Webster]

   2. Pledged; promised; especially, having the affections
      pledged; promised in marriage; affianced; betrothed.
      [1913 Webster]

   3. Greatly interested; of awakened zeal; earnest.
      [1913 Webster]

   4. Involved; esp., involved in a hostile encounter; as, the
      engaged ships continued the fight.
      [1913 Webster]

   Engaged column. (Arch.) Same as Attached column. See
      under Attach, v. t.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Engage \En*gage"\, v. t. [imp. & p. p. Engaged; p. pr. & vb.
   n. Engaging.] [F. engager; pref. en- (L. in) + gage pledge,
   pawn. See Gage.]
   1. To put under pledge; to pledge; to place under obligations
      to do or forbear doing something, as by a pledge, oath, or
      promise; to bind by contract or promise. "I to thee
      engaged a prince's word." --Shak.
      [1913 Webster]

   2. To gain for service; to bring in as associate or aid; to
      enlist; as, to engage friends to aid in a cause; to engage
      men for service.
      [1913 Webster]

   3. To gain over; to win and attach; to attract and hold; to
      draw.
      [1913 Webster]

            Good nature engages everybody to him. --Addison.
      [1913 Webster]

   4. To employ the attention and efforts of; to occupy; to
      engross; to draw on.
      [1913 Webster]

            Thus shall mankind his guardian care engage. --Pope.
      [1913 Webster]

            Taking upon himself the difficult task of engaging
            him in conversation.                  --Hawthorne.
      [1913 Webster]

   5. To enter into contest with; to encounter; to bring to
      conflict.
      [1913 Webster]

            A favorable opportunity of engaging the enemy.
                                                  --Ludlow.
      [1913 Webster]

   6. (Mach.) To come into gear with; as, the teeth of one
      cogwheel engage those of another, or one part of a clutch
      engages the other part.
      [1913 Webster]

WordNet (r) 3.0 (2006):

engaged
    adj 1: having ones attention or mind or energy engaged; "she
           keeps herself fully occupied with volunteer activities";
           "deeply engaged in conversation" [syn: engaged,
           occupied]
    2: involved in military hostilities; "the desperately engaged
       ships continued the fight"
    3: reserved in advance [syn: booked, engaged, set-
       aside(p)]
    4: (of facilities such as telephones or lavatories) unavailable
       for use by anyone else or indicating unavailability;
       (`engaged' is a British term for a busy telephone line); "her
       line is busy"; "receptionists' telephones are always
       engaged"; "the lavatory is in use"; "kept getting a busy
       signal" [syn: busy, engaged, in use(p)]
    5: (used of toothed parts or gears) interlocked and interacting;
       "the gears are engaged"; "meshed gears"; "intermeshed twin
       rotors" [syn: engaged, meshed, intermeshed]
    6: having services contracted for; "the carpenter engaged (or
       employed) for the job is sick"
    7: built against or attached to a wall; "engaged columns"