I think this essay by Dr Raymond Apple which was just pubished at Arutz Sheva website does a good job at explaining what it means to be Jewish. We have discussed this here at JTF many times, is Jewishness a religion, or is it a race, or is it a nation? Rabbi Dr Apple does a good job of trying to explain this...
http://www.israelnationalnews.com/Articles/Article.aspx/8754What is Judaism?
Iyar 9, 5769, 03 May 09 10:53
by Rabbi Dr Raymond Apple(IsraelNN.com) How should Judaism be defined? Is it a race, religion or nationality?
Despite the secularists, religion is the crucial and historically validated quality of Jewishness. 1,000 years ago, Saadia Gaon declared, "We are a people by virtue of the Torah." That is, when the people of Israel accepted the Torah as their guide-book, they gained mission, purpose and identity.
But Judaism is more than religion. That too is clear. To be a Jew is not only to be heir to a religious tradition. It is also to belong to a group, however one defines the nature of that group. Some may think it incongruous, but even an atheistic Jew remains a Jew, a member of the group.
Some people speak loosely of a "Jewish race". There is no such thing. Race is presented as a scientific concept and it simply does not apply to the Jews.
Are Jews, then, a nation? Not in any political sense, at least outside Israel. Yet, there is a wider definition of nationality or nationhood which has relevance. Some editions of the Encyclopaedia Britannica apply the term "in a more extended sense... to denote an aggregation of persons claiming to represent a racial, territorial or some other bond of unity, though not necessarily recognised as an independent political entity.... A nationality in this connexion represents a common feeling and an organised claim rather than distinct attributes."
Phrases such as "an aggregation of persons... bond of unity... common feeling..." do have their application to the Jewish people. Of this there is no doubt.
But the problem as I see it is not a straight-out one of saying: Are the Jews a religion or an ethnic group? This kind of choice hardly ever presents itself. On the whole, Jews know that both elements are part of their make-up and that they have, as Eugene B. Borowitz puts it, an "intimate fusion of peoplehood and religion."
Thus, within Jewish communal life there are times and places where the religious is stressed, notably, of course, in the synagogue; and there are places and occasions when it is the group aspect which unites us. Look for instance at the Jewish newspapers and you see that they report what Jews are doing just as much as what is doing in Judaism.
The real problem is that of deciding what image to give to the wider community. We are generally regarded as a religious denomination. Religion does not by itself cover all of Jewishness, but historically it was the religious pattern which made the Jew distinctive. Even today, whatever one's private angle on Jewish life, the vast majority of Jews maintain some religious associations and observances; and they would agree that it is Judaism which is the most Jewish of Jewish ideologies.