Secular Judaism describes the modern advent of the non-religious Jew, who engages in cultural practices and family customs but is not religious, and probably not even theistic. This describes a large proportion of Jews1,2,3, "for example, less than a third of American Jews are members of one of the religious movement into which Judaism is divided"2. Also known as "cultural Jews".3
Often the history of a people is so intertwined with their religious beliefs that it is difficult to separate their name as a people from the name of their religion. A person can be Jewish because of their family heritage or because of their religious beliefs. So, secular Jews and religious Jews are both called "Jews", and there is no way for an outsider to know if any given Jew is religious or not. Judaism as a religion, including its rites and rituals, is tied up with being a Jew culturally. The self-identity of natural Jews is tied to the religious trappings of Judaism whether or not people continue to believe in the religion itself. In the modern world life is much more compartmentalized so that modern Western religions are distinct from culture, but with older religions this distinction is not part of the world view, and so older religions tend to also be synonymous with cultural practices.
“It is important to understand that a great many Jews have little connection to Judaism as a religion. While many Jews want to maintain their Jewish identity, the majority are secular Jews with little interest in the beliefs and practices of Judaism. For example, less than a third of American Jews are members of one of the religious movement into which Judaism is divided.”
Many of these non-religious Jews still identify themselves as Jews on official forms and questionnaires, so confounding people who attempt, like me, to understand religion and count those who believe.
“There are many Jews who describe themselves as secular but who take part in activities which are, on the face of it, religious. [...] A professor from the Hebrew University in Jerusalem remarked that some people want to take part in secular celebrations of Jewish festivals, while others 'want to get away from religion entirely'”
Pilkington, as part of his introductory chapter on how Judaism is a difficult religion to quantify, shows that the Jewish religious practices are part of a culture of Jewishness that is accepted independently of the beliefs themselves. So, secular Jews still participate in Jewish "religious" festivals for cultural reasons despite not having Jewish beliefs. This makes it seem that there are more Jewish believers than there are. It is hard to count atheists worldwide, when Jewish and Christian atheists, for example, continue to call themselves Jews and Christians for cultural and traditional reasons.
This effect, of the growth of the non-religious even within religious communities, is part of the secularisation process. See: Secularisation Theory: Will Modern Society Reject Religion? What is Secularism?.
Jews get counted as 'religious' and 'theist' by pollsters without considering what the individual's actual beliefs are. See: Institutionalized Religions Have Their Numbers Inflated by National Polls.