The Collaborative International Dictionary of English v.0.48:

Synagogue \Syn"a*gogue\, n. [F., from L. synagoga, Gr. ? a
   bringing together, an assembly, a synagogue, fr. ? to bring
   together; sy`n with + ? to lead. See Syn-, and Agent.]
   1. A congregation or assembly of Jews met for the purpose of
      worship, or the performance of religious rites.
      [1913 Webster]

   2. The building or place appropriated to the religious
      worship of the Jews.
      [1913 Webster]

   3. The council of, probably, 120 members among the Jews,
      first appointed after the return from the Babylonish
      captivity; -- called also the Great Synagogue, and
      sometimes, though erroneously, the Sanhedrin.
      [1913 Webster]

   4. A congregation in the early Christian church.
      [1913 Webster]

            My brethren, . . . if there come into your synagogue
            a man with a gold ring.               --James ii.
                                                  1,2 (Rev.
                                                  Ver.).
      [1913 Webster]

   5. Any assembly of men. [Obs. or R.] --Milton.
      [1913 Webster]

WordNet (r) 3.0 (2006):

synagogue
    n 1: (Judaism) the place of worship for a Jewish congregation
         [syn: synagogue, temple, tabernacle]

Easton's 1897 Bible Dictionary:

Synagogue
   (Gr. sunagoge, i.e., "an assembly"), found only once in the
   Authorized Version of Ps. 74:8, where the margin of Revised
   Version has "places of assembly," which is probably correct; for
   while the origin of synagogues is unknown, it may well be
   supposed that buildings or tents for the accommodation of
   worshippers may have existed in the land from an early time, and
   thus the system of synagogues would be gradually developed.

     Some, however, are of opinion that it was specially during the
   Babylonian captivity that the system of synagogue worship, if
   not actually introduced, was at least reorganized on a
   systematic plan (Ezek. 8:1; 14:1). The exiles gathered together
   for the reading of the law and the prophets as they had
   opportunity, and after their return synagogues were established
   all over the land (Ezra 8:15; Neh. 8:2). In after years, when
   the Jews were dispersed abroad, wherever they went they erected
   synagogues and kept up the stated services of worship (Acts
   9:20; 13:5; 17:1; 17:17; 18:4). The form and internal
   arrangements of the synagogue would greatly depend on the wealth
   of the Jews who erected it, and on the place where it was built.
   "Yet there are certain traditional pecularities which have
   doubtless united together by a common resemblance the Jewish
   synagogues of all ages and countries. The arrangements for the
   women's place in a separate gallery or behind a partition of
   lattice-work; the desk in the centre, where the reader, like
   Ezra in ancient days, from his 'pulpit of wood,' may 'open the
   book in the sight of all of people and read in the book of the
   law of God distinctly, and give the sense, and cause them to
   understand the reading' (Neh. 8:4, 8); the carefully closed ark
   on the side of the building nearest to Jerusalem, for the
   preservation of the rolls or manuscripts of the law; the seats
   all round the building, whence 'the eyes of all them that are in
   the synagogue' may 'be fastened' on him who speaks (Luke 4:20);
   the 'chief seats' (Matt. 23:6) which were appropriated to the
   'ruler' or 'rulers' of the synagogue, according as its
   organization may have been more or less complete;", these were
   features common to all the synagogues.

     Where perfected into a system, the services of the synagogue,
   which were at the same hours as those of the temple, consisted,
   (1) of prayer, which formed a kind of liturgy, there were in all
   eighteen prayers; (2) the reading of the Scriptures in certain
   definite portions; and (3) the exposition of the portions read.
   (See Luke 4:15, 22; Acts 13:14.)

     The synagogue was also sometimes used as a court of
   judicature, in which the rulers presided (Matt. 10:17; Mark
   5:22; Luke 12:11; 21:12; Acts 13:15; 22:19); also as public
   schools.

     The establishment of synagogues wherever the Jews were found
   in sufficient numbers helped greatly to keep alive Israel's hope
   of the coming of the Messiah, and to prepare the way for the
   spread of the gospel in other lands. The worship of the
   Christian Church was afterwards modelled after that of the
   synagogue.

     Christ and his disciples frequently taught in the synagogues
   (Matt. 13:54; Mark 6:2; John 18:20; Acts 13:5, 15, 44; 14:1;
   17:2-4, 10, 17; 18:4, 26; 19:8).

     To be "put out of the synagogue," a phrase used by John (9:22;
   12:42; 16:2), means to be excommunicated.