Answer:
   
   A synagogue is a Jewish place of assembly for worship, education, and
   communal affairs. One tradition dates synagogues back to the
   Babylonian exile of the 6th cent. BCE, when the returnees may have
   brought back with them the basic structure that was to be developed by
   the 1st cent. CE into a well-defined institution around which Jewish
   religious, intellectual, and communal life was to be centered. Other
   scholars believe the synagogue arose after the Hasmonean revolt
   (167-164 BCE) as a Pharisaic alternative to the Temple cult. In any
   case, the destruction of the Temple (70 CE) and the Diaspora over the
   following centuries increased the synagogue's importance.
   
   Services in the synagogue were conducted in a simpler manner than in
   the historic Temple. Services were conducted by a chazzan (reader), as
   opposed to a formally appointed priest. Some congregations today
   continue to use a chazzan, but in most, services are led by a rabbi.
   
   The place of Jewish worship has many names. The Hebrew term is beit
   k'nesset (literally, House of Assembly). Many people use the word
   "shul," which is a Yiddish word derived from a German word meaning
   "school" (which demonstrates the synagogue's role as a place of
   study). "Synagogue" is a Greek translation of Beit K'nesset and also
   means "place of assembly" (related to "synod"). Progressive Jews often
   use the word "temple," because they consider every one of their
   meeting places to be equivalent to, or a replacement for, the Temple
   (this usage offends some traditional Jews, because they believe there
   was only one Temple). Lastly, some Jews just use the term
   "Congregation".
   
   Note that the word "Temple" is often used to refer to the place in
   Jerusalem that was the center of Jewish religion from the time of
   Solomon to its destruction by the Romans in 70 CE. According to
   tradition, this is the one and only place where sacrifices and certain
   other religious rituals were performed. It was partially destroyed at
   the time of the Babylonian Exile and rebuilt ("the Second Temple").
   The "Wailing Wall" is the western retaining wall of that Temple, and
   is as close to the site of the original Sanctuary as Jews can go
   today. Traditional Jews believe that The Temple will be rebuilt when
   the Moshiach (Messiah) comes.
   
   Also, note that a synagogue serves many purposes. It is a house of
   prayer, of course, because people go there to pray in group prayer. It
   is a house of assembly, because people assemble there for social
   events, such as dinners, fundraisers, and other non-religious
   activities. It is a house of study because life-long learning is a
   part of Judaism: we teach our children there, and we teach ourselves
   there through adult education.