The Collaborative International Dictionary of English v.0.48:

Engagement \En*gage"ment\, n. [Cf. F. engagement.]
   1. The act of engaging, pledging, enlisting, occupying, or
      entering into contest.
      [1913 Webster]

   2. The state of being engaged, pledged or occupied; specif.,
      a pledge to take some one as husband or wife.
      [1913 Webster]

   3. That which engages; engrossing occupation; employment of
      the attention; obligation by pledge, promise, or contract;
      an enterprise embarked in; as, his engagements prevented
      his acceptance of any office.
      [1913 Webster]

            Religion, which is the chief engagement of our
            league.                               --Milton.
      [1913 Webster]

   4. (Mil.) An action; a fight; a battle.
      [1913 Webster]

            In hot engagement with the Moors.     --Dryden.
      [1913 Webster]

   5. (Mach.) The state of being in gear; as, one part of a
      clutch is brought into engagement with the other part.

   Syn: Vocation; business; employment; occupation; promise;
        stipulation; betrothal; word; battle; combat; fight;
        contest; conflict. See Battle.
        [1913 Webster]

WordNet (r) 3.0 (2006):

engagement
    n 1: a hostile meeting of opposing military forces in the course
         of a war; "Grant won a decisive victory in the battle of
         Chickamauga"; "he lost his romantic ideas about war when he
         got into a real engagement" [syn: battle, conflict,
         fight, engagement]
    2: a meeting arranged in advance; "she asked how to avoid
       kissing at the end of a date" [syn: date, appointment,
       engagement]
    3: a mutual promise to marry [syn: betrothal, troth,
       engagement]
    4: the act of giving someone a job [syn: employment,
       engagement]
    5: employment for performers or performing groups that lasts for
       a limited period of time; "the play had bookings throughout
       the summer" [syn: engagement, booking]
    6: contact by fitting together; "the engagement of the clutch";
       "the meshing of gears" [syn: engagement, mesh, meshing,
       interlocking]
    7: the act of sharing in the activities of a group; "the teacher
       tried to increase his students' engagement in class
       activities" [syn: engagement, participation,
       involvement, involution] [ant: non-engagement, non-
       involvement, nonparticipation]

Moby Thesaurus II by Grady Ward, 1.0:

212 Moby Thesaurus words for "engagement":
   Olympic games, Olympics, absorbed attention, absorption, action,
   affair, affiance, agreement, allurement, alternation, application,
   appointment, arrangement, assignation, association, attempt, banns,
   banns of matrimony, bargain, battle, berth, bespeaking, betrothal,
   betrothing, betrothment, billet, blandishment, blind date, booking,
   borscht circuit, bout, briefing, business, cajolement, cajolery,
   circuit, coaction, coaxing, cochairmanship, combat, commission,
   commitment, complementary distribution, complicity, concentration,
   concours, concurrence, condominium, conflict, conning,
   contemplation, contest, contract, contribution, cooperation,
   copartnership, copartnery, cotenancy, covenant, date, deal,
   deep study, deep thought, derby, double date, effort,
   embarrassment, employment, encounter, engagement book, engaging,
   engrossment, enlistment, enmeshment, entanglement, enterprise,
   espousal, exhortation, fight, game, games, get-together, gig, go,
   gymkhana, handfasting, having a part, hiring, hortation, immersion,
   implication, inclusion, incumbency, inducement, intentness,
   interaction, interchange, intercommunication, intercourse,
   interlacing, intermeshing, interplay, intertwining, interview,
   interweaving, interworking, invitation, involution, involvement,
   jawboning, job, joint chairmanship, joint control, joint ownership,
   joint tenancy, joust, lobbying, marriage contract,
   marriage proposal, match, matching, meditation, meet, meeting,
   mesh, meshing, monomania, moonlighting, obligation, obsession,
   offer of marriage, office, opening, operation, partaking,
   participation, partnership, persuasion, place, plan,
   playing engagement, pledge, plight, plighted faith, plighted troth,
   position, post, preaching, preachment, preengagement,
   preoccupation, profound thought, program, project, promise,
   proposal, proposition, quid pro quo, rally, rapt attention,
   recognizance, relation, rencontre, rendezvous, reservation,
   retainment, run, sales talk, salesmanship, second job, seesaw,
   selling, service, sharing, single-mindedness, situation, snow job,
   soft soap, solicitation, spot, stand, station, studiousness, study,
   suasion, submersion, suffrage, sweet talk, taking on, task, tenure,
   test, tilt, tit for tat, tour, tournament, tourney, trial, troth,
   tryst, understanding, undertaking, vacancy, vaudeville circuit,
   venture, verbal agreement, visit, voting, wheedling, word, work,
   working on