Well, I know now exactly what they meant, because within the first week of living here I felt secular in a way I would never have thought possible in the U.S. In the U.S., my "Shabbat-Respectful" reply to the question of "do you observe Shabbat?" was typically sufficient to convey that, though I wasn't shomer Shabbos, I did typically either attend Friday night services, light the candles at home, OR go to a Shabbat dinner somewhere in the community. Indeed, my religous observance, as minimal as it was, was much greater in the past several years than it was thoughout my childhood and early adulthood. Certainly through the eyes of many friends and my family, I was "the religious one"....the one that wished my family a Shabbat Shalom, the one who led our family's Passover Seder, and the one who would be found celebrating, in some manner, the holidays - Shavout, Simcha Torah, Purim, etc. - that aren't always on the proverbial American secular Jewish radar.
In Israel, by contrast, its a pretty clear case. While I'll likely join one of the few Conservative or Reform Jewish communities in the area and carry on the same level of observance that I did in the states, I know that I won't be shomer Shabbos, won't wear a kippah or or display Tzitit. I won't lay tefillin, nor regularly attend services. I am, at heart, a secular Zionist...a secular Israeli. But, digging further into it, I think I have an understanding about my view of Judaism in the U.S. (in the diaspora), and why its somewhat different living in Israel.
In the U.S., as a represetative of a religious minority representing less than 2% of the population - a population, due to various demographic factors within our community, which is stagnant at best, and where our future survival as a distinct religious community is in doubt to some degree -I felt the responsibility to maintain the traditions not only for me and my family, but for my future children (G-d willing) and for future generations of Jews to come.
I said to someone very close to me a couple years ago that I feel very protective of Judaism. And, while I certainly had no doubt that I loved being Jewish independent of any danger or threat, I probably did cling more tightly to the path than I would have if I didn't feel that our future was so precarious.
Now, as a Jew in a majority Jewish country with no shortage of observant Jews to carry on, and pass to futre generations, a love and fidelity to our religious traditions (to observe the Mitzvot), I feel perhaps a bit more free to be the Jew that I feel most comfortable being - one consumed with a passion to preserve and protect the Zionist project (the national liberation movement of a people who have built a state where Jews are free to be whatever Jew they wish to be.)
Amusingly, my mother once expressed this half-kidding fear that I would return to the U.S. one day as a "black hatter". (Orthodox Jew who wears traditional black hat, black coat, black trousers, black tie, beard and curls, etc.) While I knew then, and now know for sure, that this will never happen, I am tempted to play a joke on her when I greet her after returning to the U.S., and might be seen shopping in Me'a She'arim shortly before my flight!
Update on April 27, 2010:
As I married Chana, who happens to be religious, in March, and have taken to wearing a Kippah everyday, perhaps the characterization of myself as "secular" was a bit, let's just say, premature:)