Thayer's Greek Lexicon

 1. a bringing together, gathering (as of fruits), a contracting
2. in the NT, an assembling together of men, an assembly of men
3. a synagogue
  1) an assembly of Jews formally gathered together to offer
prayers and listen to the reading and expositions of the
scriptures; assemblies of that sort were held every sabbath
and feast day, afterwards also on the second and fifth days of
every week; name transferred to an assembly of Christians
formally gathered together for religious purposes
  2) the buildings where those solemn Jewish assemblies are held.
Synagogues seem to date their origin from the Babylonian
exile. In the times of Jesus and the apostles every town, not
only in Palestine, but also among the Gentiles if it contained
a considerable number of Jewish inhabitants, had at least one
synagogue, the larger towns several or even many. These were
also used for trials and inflicting punishment.