How were synagogues and the rabbis related?

Synagogues are the Jewish houses of prayer; and Rabbis are the leaders of the Jewish communities. Most synagogues were and are guided by one or more Rabbis. The Rabbis (Torah-sages) spelled out the importance of praying in synagogue (public prayer) as part of living according to Judaism (Talmud, Berakhot 7b-8a). In addition, many synagogues have also functioned as places of Torah-learning, which is led by Rabbis who teach Torah to scholars and members of the laity. See also the Related Links.

Link: More about Jewish prayer

Link: History of synagogue-prayer