‘Jewish Identity’ refers to the way Jews see themselves.
For example, one person might consider themselves Jewish only or primarily because their parents are Jewish. Someone else might be Jewish (according to other Jews) because their parents are, but feel like they have no religious or ethnic identity. In this case we might say that they have very little self-identity as Jews, and their only Jewish identity comes from the way others view them.
At its bare minimum, Jewish identity consists of the act of claiming to be part of the Jewish community.
Religious/Secular/Zionist/Cultural Jewish Identities
There are several different ways that people relate to their Jewish heritage, and most people have a mixture of elements of Jewish identity. The key dichotomy in the modern world is between those who see Judaism as a religion and themselves as somewhere between religious and secular, and those who view Judaism as an ethnic or national identity, like being Greek Australian or Chinese Australian.
Religious Jews relate to Judaism as a total way of life which provides them with rules and structure for every waking moment. It guides them in getting out of bed, dealing with shopkeepers, praying to God, raising a family and all matters in between.
People who are less religious but also not particularly aligned with Judaism as an ethnicity made up the majority of Jews in Australia in the 19th century. They saw themselves as Australians of the Jewish persuasion. In everything except the kind of house of worship these Jews believed that they were indistinguishable from other Australians.
Secular Zionist Identity
With 19th century Zionism and the establishment of the State of Israel in the 20th century, a new category of affiliation was created: the secular Israeli or the secular Zionist living outside Israel. To these Jews it is the nation of Israel, or the people of Israel (Am Yisrael in Hebrew) that has their loyalty.
They view Jews as consistently a nation apart, held together in dispersion for almost two thousand years by a common language, Hebrew; a common destiny; and a common land, Israel. Jews living outside Israel might indicate their affiliation by supporting Israel financially or by lobbying on her behalf.
Cultural identity is that based on the customs and lifestyle of the Jewish community. This identity shifts depending on whether the person is of Ashkenazi, Sephardi or other ethnic background; Eastern or Western in orientation. To cultural Jews whose grandparents immigrated to Australia from Russia, gefilte fish and bagels will always remind them of home, and reinforce their Jewish identity. To a Syrian Jew, the identification might be with kibbe.
Jews consider themselves to be cultural in their identity when they patronise Jewish bookstores, play Jewish music, identify with Jewish history, speak a Jewish language or eat Jewish-style food.