The Collaborative International Dictionary of English v.0.48:

Archbishop \Arch`bish"op\, n. [AS. arcebisceop, arcebiscop, L.
   archiepiscopus, fr. Gr. 'archiepi`skopos. See Bishop.]
   A chief bishop; a church dignitary of the first class (often
   called a metropolitan or primate) who superintends the
   conduct of the suffragan bishops in his province, and also
   exercises episcopal authority in his own diocese.
   [1913 Webster]

WordNet (r) 3.0 (2006):

archbishop
    n 1: a bishop of highest rank

Moby Thesaurus II by Grady Ward, 1.0:

36 Moby Thesaurus words for "archbishop":
   Grand Penitentiary, Holy Father, abuna, antipope, archdeacon,
   archpriest, bishop, bishop coadjutor, canon, cardinal,
   cardinal bishop, cardinal deacon, cardinal priest, chaplain,
   coadjutor, curate, dean, diocesan, ecclesiarch, exarch, hierarch,
   high priest, metropolitan, papa, patriarch, penitentiary, pontiff,
   pope, prebendary, prelate, primate, rector, rural dean, subdean,
   suffragan, vicar



Bouvier's Law Dictionary, Revised 6th Ed (1856):

ARCHBISHOP, eccl. law. The chief of the clergy of a whole province. He has
the, inspection of the bishops of that province, as well as of the inferior
clergy, and may deprive them on notorious cause. The archbishop has also his
own diocese, in which he exercises, episcopal jurisdiction, as in his
province he exercises archiepiscopal authority. 1 Bl. Com. 380; L. Raym.
541; Code, 1, 2.



The Devil's Dictionary (1881-1906):

ARCHBISHOP, n.  An ecclesiastical dignitary one point holier than a
bishop.

    If I were a jolly archbishop,
    On Fridays I'd eat all the fish up --
    Salmon and flounders and smelts;
    On other days everything else.
                                                              Jodo Rem