An Atheist Jew is a member of the Jewish community who does not believe in God but still considers himself a Jew and perhaps retains some of the customs of the Jewish faith.
For example, to an Atheist Jew, the Menorah represents the infinite power of the Jewish spirit. No mention of a divine force in Jewish history would be accepted literally; the Torah is viewed as a common mythology of the Jewish people, not a faith document or correct history.