Question: "What is the significance of a kippah / yarmulke?"
Answer: The kippah (plural: kippot) or yarmulke/yamaka (Yiddish) is a skullcap, a small, round head covering worn by Jews—mostly men. The kippah was first mentioned in the 24-chapter Tractate Shabbat, one of 12 books in the Moed Order—the section of the Mishnah on festivals. The book concentrates on those activities that are forbidden on the Sabbath, like talking about business and carrying things. The exact origin and purpose of the yarmulke is unclear, but it’s used as a sign of respect to God: the wearer of the kippah acknowledges that God is above him. Some Jewish teachers insist that men cover their heads during prayer (which apparently contradicts the beliefs in Jesus’ time, according to 1 Corinthians 11:7) and other religious studies. Some say a yarmulke must be worn at all times, even when sleeping. Others say that wearing a kippah is an exceptional practice of piety and is not required for the general public. In some Reform and Conservative Jewish circles, women wear yarmulkes, as well.
Today, the type of yarmulke can also represent the wearer’s sect and political leaning. Ultra-Orthodox Jews have large, black yarmulkes made of velvet. More modern Jews wear lighter colors. Black silk is used by those who aren’t devout or by non-Jews who wish to observe customs while visiting a synagogue. Zionists often wear crocheted or knitted yarmulkes. A hat can be worn over the yarmulke as a kind of double-dose or in lieu of a yarmulke when displaying one’s Jewish heritage isn’t wise. Conversely, some yarmulkes come in sports team colors or even cartoon characters. A famous story says that when a Navy Rabbi used his yarmulke to wipe the blood from victims of the Beirut barracks bombing in 1983 a fellow chaplain, a Catholic priest, tore off a piece of his uniform to create a make-shift yarmulke.
Yarmulkes are not mentioned in the Bible, and wearing a kippah is not commanded in the Mosaic Law. Yarmulkes weren’t mentioned until about 200 years after the time of Jesus, in the Mishnah (the extra-biblical teachings that gave unnecessary specifics on how to follow the Law). They didn’t become common until the Middle Ages. Kippot obviously aren’t required for Christians, but it would be polite to wear one when visiting a synagogue or taking part in a Jewish ceremony.