A. To tell the truth, Yarmulka (from the Talmudic phrase: “fear of the king”) or Kippa (which means (domed) covering) is not a Mitzvah of Torah or Rabbinic origin (outside of prayer) though the Talmud does mention its importance. Which is why it’s OK for many Jews to wear it only during prayer or special Jewish events.
But because it is an expression of Jewish identity, and a constant reminder that G-d is above us, it is the custom of many Jews to wear it all the time. In fact in some circles, as with the Orthodox community in a major metro Jewish area like NYC where it is more accepted and expected, not wearing one makes you stand out.
It represents that there is something (G-d) that’s above us (our heads) and it is a sign of respect and awe. It reminds us that our desires and even our intellect are not the final say. I think what’s most important is that nowadays, it has come to mean: Hey. I’m Jewish and I’m proud of it! – which is why many folks don’t want to take it off, because we really want to stay connected with our Jewishness at all times. But not wearing it all the time, is surely no sign of any disrespect or alienation.