What relationship does the nation of Israel have to Jewish identity?
Right now, the nation of Israel is having something of a dilemma about its relationship with the Jewish faith. Specifically, the nation is having to decide whether it is specifically a Jewish nation or whether it is a democratic nation that happens to have a population that is mostly made up of Jews.
Right now, the Israeli government is proposing a change to the oath that new immigrants must swear. They are proposing that the new immigrants must swear allegiance to the "nation-state of the Jewish people." This is being interpreted as requiring people to acknowledge the idea that Israel is an inherently Jewish state. (See Reuters link...)
Under this view, the relationship between Jewish identity and Israel is that Israel is a Jewish state and that Jewish identity is an inalienable part of what Israel is.
If you are talking about the importance of Israel to Jewish identity, please look at the other link. Traditionally, attachment to the idea of Israel has been a major aspect of Jewish faith ("next year in Jerusalem" as a traditional line at a Passover feast). But lately, this has become somewhat more problematic as Israel becomes increasingly Orthodox and its values become different from those of many of the Diaspora.