Kippot
The most commonly known and recognized piece of Jewish garb is actually the one with the least religious significance. The word yarmulke (usually, but not really correctly, pronounced yammica) is Yiddish. According to Leo Rosten's The Joys of Yiddish, it comes from a Tartar word meaning skullcap. According to some Orthodox and Chasidic rabbis I know, it comes from the Aramaic words "yerai malka" (fear of or respect for The King). The Hebrew word for this head covering is kippah (pronounced key-pah).
It is an ancient practice for Jews to cover their heads during prayer. This probably derives from the fact that in Eastern cultures, it is a sign of respect to cover the head (the custom in Western cultures is the opposite: it is a sign of respect to remove one's hat). Thus, by covering the head during prayer, one showed respect for G-d. In addition, in ancient Rome, servants were required to cover their heads while free men did not; thus, Jews covered their heads to show that they were servants of G-d. In medieval times, Jews covered their heads as a reminder that G-d is always above them. Whatever the reason given, however, covering the head has always been regarded more as a custom rather than a commandment.
There is no special significance to the yarmulke as a specific type of head covering. Its light weight, compactness and discreteness make it a convenient choice of head gear. I am unaware of any connection between the yarmulke and the similar skullcap worn by the Pope.