Why do Jews belong to synagogues?

Answer 1

Jewish communities don't actually require a synagogue as community prayer can take place anywhere. In some communities, the 'synagogue' is in someone's home. Synagogues are established as a place for community worship, gatherings, and study.

Answer 2

Synagogues traditionally have played a central role in Jewish life, just as churches and mosques have played an important role in Christian and Muslim life. They are not only centers of prayer, but of learning and study, of community and connection, including childhood and adult education as well as social activities such as arts, crafts, lectures, concerts and other community events. Because synagogues are buildings built on land and are generally not funded by any central authority, they cost money, to build, to maintain, to staff. So membership in and dues paid to a congregation helps support the facility and its work.

Synagogues also join together in relatively loose confederations; one for example for Reform Synagogues is the UAHC - Union of American Hebrew Congregations. These organizations are able to then help manage and promote content and consistency and provide additional services such as rabbinical schools, religious school curricula, summer camps, publication needs (prayer books, school books, etc.), other kinds of coordinated efforts including support for Israel, and a greater presence for the overall community politically than a single congregation could make.

On the other hand, technically wherever one can find ten Jewish adults, a prayer service is considered "official". And this does not prevent Jews from individual prayer. But the historical role of the synagogue is to emulate the great Temple of Solomon in Jerusalem as the Jewish people have moved into diaspora (spreading out over many lands outside the historic home of the Jewish people in Israel).