The kippah (or koppel/yarmulke in Yiddish) is the most obvious outward sign of Jewishness. Unlike Christians, who bear their heads as an expression of respect, Jews cover theirs.
The kippah became normative quite late, but back in talmudic days head covering was a sign of piety. Talmud Shabbat (156b) tells how, when Rabbi Nachman bar Yitzchak was born, the star-gazers said he would grow up to be a thief. His mother then decided to cover his head all the time. It obviously worked because he became a rabbi. Shabbat 118b says that Rav Huna never walked more than four amot (about six feet) without a head covering.
The 16th-century Shulchan Aruch was the first to rule that wearing a kippah was mandatory and not merely customary. Today wearing a kippah is not just about piety or humility; it also bears an element of Jewish pride and belonging. Outside of Israel, whether one feels comfortable wearing a kippah in a place is a pretty good indication of the degree to which Jews there feel safe.
Rabbi Julian Sinclair