A 'yarmulke (Hebrew: יאַרמלקע meaning "cap") is a thin, slightly-rounded skullcap traditionally worn by Orthodox Jewish men, although some men and women in the egalitarian Conservative and Reform movements also wear it during services. Wearing a Yarmulke is described as "honoring God." According to the Talmud, a Jewish man is required to cover his head during prayer. The Yarmulke has become identified as a symbol of Judaism over the last century. It is also known as a kippah (Hebrew: כִּפָּה kippa, plural kippot .קאַפּעלע kapele.)
Many religions imbue clothing with religious significance as a sign of respect before God. Religious vestments convey the message that daily practice requires purity and cleanliness as well as constant remembrance of the divine's blessings and commandments.
The word yarmulke is a Yiddish word, deriving from the Polish jarmułka, meaning "cap." The popular claims that it comes from an Aramaic phrase yari malka, meaning "fear of the King [i.e., God]," or from the Hebrew ya'are me-elohim, "to tremble beneath the Lord," are both without evidence. The popularity of these folk etymologies probably owes to the idea that the yarmulke is a tribute to God, an interpretation that resonates with Jews.
In Hebrew, kippah means "dome." The Goth word kappel (cf. Chapel) still exists in the Yiddish term today. The equivalent of the Hebrew word is the French calotte and the Italian calotta, both meaning an architectural dome.
Head coverings in ancient Israelite culture
The Tanakh (Hebrew Bible) makes references to special head coverings for Jewish males in biblical times, and the prevalence of this custom is supported by archeology: The Israelites on Sennacherib's marble relief appear with headdress, and although the ambassadors of Jehu on the Shalmaneser stele have a head covering, their costume seems to be Israelite. One passage of the older literature is of significance: I Kings 20:31 mentions חֲבָליִם havalim together with שַׂקּיִם saqqim, both of which are placed around the head. The ancient Israelites might have worn a headdress similar to that worn by the Bedouins, or have adopted a turban-like headdress more like that of the Fellahs of today.
The latter hypothesis is supported by the noun צַנִיף tzanif and by the verb חַבָּש habash (to wind; comp. Ezekiel 16:10; Jonah 2:6). Tzanaf means "to roll like a ball" (Isaiah 22:18). As to the form of such turbans, nothing is known; perhaps they varied according to the different classes of society, as was customary with the Assyrians and Babylonians, whose fashions may have influenced the costume of the Israelites. 
Middle Eastern and North African Jewish community headdress may also resemble that of the ancient Israelites. In Yemen, the wrap around the cap was called מַצַר massar; the head covering worn by all women according to Dath Mosha was a גַּרגוּש "Gargush." 
Codification in Jewish law
According to the Shulchan Aruch, a code of Jewish law, men are required to cover their heads and should not walk more than four cubits without one. . Wearing a Yarmulke/kippa is described as "honoring God."  The Mishna Brurah modifies this ruling, adding that the Achronim established it as a requirement to wear a head covering even when traversing less than four cubits,  and even when one is simply standing in place. This applied both indoors as well as out.
This ruling is echoed by the Kitzur Shulchan Aruch, a concise version of the Shulchan Aruch authored by Rabbi Shlomo Ganzfried. He cites a story from the Talmud (Shabbos 156b) about Rav Nachman bar Yitzchok who might have become a thief if his mother had not saved him from this fate by insisting that he cover his head, which instilled in him the fear of God.
In many communities, boys are encouraged to wear one from a young age in order to ingrain the habit. 
According to Rabbi Isaac Klein's Guide to Jewish Religious Practice, a Jew ought to cover his head when in the synagogue, at prayer or sacred study, when engaging in a ritual act, and when eating. 
The yarmulke/kippah is traditionally worn by men but today, some women, mainly Reform and Conservative Jews, wear it as well. Some Jews wear the Yarmulke only while praying, eating, reciting a blessing, or studying Jewish religious texts.
In modern contexts, it is also common for non-Jews to wear a simple kippah or cover their heads as a sign of respect when present at Jewish religious services. If a non-Jew goes to the Western Wall in Jerusalem it is required that he don a skull cap once he is near the Wall. This point is marked out by a ramp down towards the wall from the rest of the plaza and skull caps are provided to non-Jews. They are re-usable caps that are given back after usage.
Any form of head covering is acceptable according to halakha (Jewish law). There are no hard and fast rules on the subject, although the compact, lightweight nature of a kippah, may have contributed to its popularity.
Often the color and fabric of the kippah can be a sign of adherence to a specific religious movement. Haredi men, who mostly wear large black cloth or velvet kippot, often wear fedoras with their kippot underneath. In the Hassidic community, this double head-covering has Kabbalistic meaning. The Israeli Religious Zionist community is often referred to by the name kippot serugot (Hebrew כיפות סרוגות), literally "knitted kippot," though they are typically crocheted. American Modern Orthodox Jews often wear suede or leather yarmulkes, requiring clips to hold them in place. Members of most Haredi groups usually wear black velvet or cloth kippot. Because of this, men who wear these kippot are sometimes referred to as kipot shekhorot (Hebrew כיפות שחורות), literally "black kippot."
In the early nineteenth century in the United States, rabbis often wore a scholar's cap (large saucer-shaped caps of cloth, like a beret) or a Chinese skullcap. A famous Californian rabbi, the Moldavian Rabbi Benjamin ben Benjamin (Rabbi Benjamin II), is pictured in an engraved portrait wearing a Chinese silk skullcap.
Other Jews of this era wore black pillbox-shaped kippot. During the Polemic Wars in the mid-1800s, Reformers led by Rabbi Isaac Wise stopped wearing kippot altogether.
More recently, kippot have been observed in the colors of sports teams supported by the wearer, especially football. In the United States, children's kippot with cartoon characters or themes such as Star Wars are popular. (In response to this trend, some Jewish schools have banned kippot with characters that do not conform to traditional Jewish values.)
Samaritan Israelis once wore distinctive blue head coverings, to separate them from Jews who wore white ones, but today they more commonly wear fezzes with turbans similar to that of Sephardic Jews from the Middle East and North Africa. Today, Samaritans do not normally wear head coverings except during prayer, Sabbath, and religious festivals. This is thought to be a recent development brought on by the constant Jewish criticism of Samaritan habits.
Instructions for wearing a Yarmulke are found in the Talmud. Tractate Shabbat 156 B.C.E. states:
- "Cover your head in order that the fear of heaven may be upon you."
Tractate Kiddushin 31a states:
- "Rabbi Honah ben Joshua never walked 4 cubits (2 meters) with his head uncovered. He explained: "Because the Divine Presence (Shekhina) is always over my head."
Some Jews wear two head coverings, typically a kippah covered by a hat, for Kabbalistic reasons: the two coverings correspond to two levels of intellect, or two levels in the fear of God. The High Priest of the Temple in Jerusalem, the Kohein Gadol, also used to wear a woolen kippah under his priestly headdress (Talmud Chulin 138a). 
As to the obligation of wearing a yarmulke, halakhic experts agree that it is a custom. The prevailing view among Rabbinical authorities is that this custom has taken on a force of law (Shulkhan Arukh, Orach Chayim 2:6), because it is an act of Kiddush Ha-Shem, "Sanctifying the Holy Name." From a strictly Talmudic point of view, the only moment when a Jewish man is required to cover his head is during prayer (Mishne Torah, Ahavah, Hilkhot Tefilah 5:5). However, even this interpretation is in question since as recently as the 1600s, scholar David Haley of Ostrog, Russia, suggested that Jews should never uncover their heads, in order to help distinguish them from Christians—especially while at prayer.
One Kabbalist tradition states that the kippah reflects the idea that Ha-Shem (God) covers us with His Divine Palm; indeed, the Hebrew word kaf means either "cloud" or "palm of the hand." The Hebrew letter kav is the first letter of the word kippah.
Reasons given for wearing a yarmulke today include:
- recognition that God is "above" humankind;
- "acceptance" of the 613 mitzvot (commandments);
- "identification" with the Jewish people;
- demonstration of the "ministry" of all Jews.
Buddhist priests in China wear the bao-tzu (more commonly known as the mao-tzu, 帽子 Mandarin màozi), the classic skullcap that is the most like the Jewish tradition. In Japan, the cap is more in the form of a pillbox and is called the boshi (帽子). Though not of ecclesiastical significance, the Buddhist skullcap does denote the priest's standing in the community.
The zucchetto (Italian for "small gourd") of the Roman Catholic Church is based on a very old kippah design. The cap is traditionally worn by clergy members and its color denotes the rank of the wearer: the Pope wears a white cap; the Cardinals red; Bishops, as well as abbots and prelates, violet; Deacons and Priests, black, although this practice is very rare among diocesan and religious order priests.
The usage of the cap was borrowed from the Jews as a custom, sometime around the fifth century C.E.—but during the early days of the Inquisition it was also a most useful tool for identifying Jews: Catholic clerics have always removed the zucchetto in the presence of their superiors, while Jews will never remove or doff their kipot. Furthermore, the Catholic laity may not wear a skullcap, while all Jews may wear one.
Among followers of the Druze faith, the use of headgear is similar to Judaism, although some Druze also wear either the fez, a fez-turban combination, or the pillbox skullcap (known as the Bokhara, after the city of Bokhara in Khazakstan).
Many Muslims wear a kippah equivalent called a topi or kufi following the example of the Prophet Muhammad to cover one's head. The doppa, a square or round skullcap originating in the Caucasus and worn by Kazan Tatars, Uzbeks and Uyghurs is another example of a Muslim skullcap. The doppa is derived from a Turkic, more pointed ancestral cap, which can be seen in some of the portraits of Jalaleddin Mingburnu.
Conservative Muslims in Malaysia, especially in the rural areas, are often seen wearing a thin kopiah, which looks almost exactly like the kippah in outward appearance.
Switzerland is home to the Cup-and-Ring (or Kuppa-unt-Hinge) skullcap, a straw cap with embroidered flowers, a small pompom in the center, and velvet strips sewn round it in rings. This cap was traditionally worn by shepherds for luck and by married men (for fertility).
Although not a skullcap per se, the Sikh Turban fulfills a similar role as the Jewish Yarmulke by showing respect before God. Wearing a Turban is viewed as sign of respect, honour, and devotion in the presence of God's creation.
The black satin head gear called a fenta or topi is a pillbox-shaped skullcap, worn by Zarathushtris Zoroastrians. Like the doppah, it is possible that the fenta/topi may have had influence on the use of the kippa. It is considered in the Zarathushtri religion to be of vital importance in the attainment of Urvaan, the Zoroastrian equivalent of Buddhist Nirvana. In earlier times, a very saucer-shaped, red and white striped kipah was the hallmark of the Zarathushtri.