What is Jewish Kippah

The Kippah (Skullcap)
A kippah (literally: dome) is the Hebrew word for skullcap, also referred to in Yiddish as a yarmulke, or less frequently as a koppel. Jewish law requires men to cover their heads as a sign of respect and reverence for G-d when praying or speaking G-d's name while reciting a blessing, during study, and while in a synagogue or yeshiva. This practice has its roots in biblical times, where the priests in the Temple were instructed to cover their heads. Traditionally, Jewish men and boys wear the kippah at all times, a symbol of their awareness of, and submission to, a "higher" entity. There is no requirement either biblically nor explicitly stated in the Talmud that this practice be followed although the practice is noted in the Talmud. Yet, through the ages it became an accepted Jewish custom, which, according to the majority of halachic authorities, makes it mandatory. One should, therefore, not walk or even sit, bareheaded. Small children should also be taught to cover their heads.
Even those who do not wear a head covering at all times, will cover it as a sign of respect when attending religious services such as at a cemetery, a shiva house, or a wedding. Many Jewish men and boys wear a kippah even while wearing a hat. The rational is that when the hat is removed either for comfort or politeness, the head remains covered. 
While most chassidic Jews wear the traditionalblack kippah, many Jews will wear kippot (plural form of kippah) of various colors or designs. During the High Holidays, many wear white kippot. Some communities have developed kippah designs that are highly intricate works of art. Some of the best known are made by Jewish artisans from Yemen and Georgia, most of whom now live in Israel.

 
Kippah as identification 
Often the color and fabric of the kippah can be a sign of adherence to a specific religious movement. The Israeli Religious Zionist community is often referred to by the name kippot serugot, literally "knitted kippot," though they are typically crocheted. American Modern Orthodox Jews often wear suede or leather kippot which require 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, literally "black kippot".
In the early 19th 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. An engraved portrait of the Moldavian rabbi, Benjamin ben Benjamin (Rabbi Benjamin II), shows him wearing a Chinese silk skullcap.
Other Jews of this era wore black pillbox-shaped kippot. 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.)
Some Breslov Hasidim, known commonly as "the Na-Nach Breslovers" the followers of the late Rabbi Yisroel Ber Odesser, wear full-head-sized, white, crocheted kippot with the Na Nach Nachma Nachman Meuman mantra emblazoned on it. Mainstream Breslover Hasidim (the larger percentage of the Breslov community who do not follow Rabbi Yisrael Ber Odesser) dress like other Hasidim with black velvet kippot.
Samaritan Israelis once wore distinctive blue head coverings to separate them from Jews who wore white ones, but today they more commonly wear fezes with turbans similar to that of Sephardi Jews from the Middle East and North Africa. Today, Samaritans don't normally wear head coverings except during prayer, Sabbath, and religious festivals.

 
Kippah Traditions 
The kippah is traditionally worn by Jewish men. Observant Jewish women who have been married (including widows and divorcees) cover their heads more completely with scarves, hats, or wigs, but for a totally different reason. The tradition for women comes from a different source than that of men and originates from the laws dealing with the sotah, implying that a Jewish married woman should cover her hair under normal circumstances. Today, some women — mainly Reform and Conservative Jews — wear a kippah. Some Jews wear kippot only while praying, eating, reciting a blessing, or studying Jewish religious texts.
In modern contexts, it is also common for non-religious Jews or even non-Jews to wear a simple kippah, or to cover their heads as a sign of respect, when present at Jewish religious services or at ostensibly Jewish sites, such as Yad Vashem and the Western Wall. Male Jews and non-Jews alike are asked to don a skullcap in the vicinity of the Western Wall, and returnable skullcaps are provided for this use.
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, along with the fact that hats for men have fallen out of fashion in the West over last few decades, may have contributed to its popularity. Kippot have become identified as a symbol of Judaism over the last century. Haredi men, who mostly wear large black cloth or velvet kippot, often wear fedoras with their kippot underneath. In the Hasidic community, this double head-covering has Kabbalistic meaning.

 
Head coverings in ancient Israelite culture 
The Tanach (The Hebrew Bible) makes references,at times, to special head coverings for Jewish males over the age of 12 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 havalim together with saqqim, both of which are placed around the head. This calls to mind pictures of Syrians on Egyptian monuments, represented wearing a cord around their long, flowing hair, a custom still followed in Arabia. Evidently the costume of the poorest classes is represented; but as it gave absolutely no protection against the heat of the sun to which a worker in the fields is so often exposed, there is little probability that it remained unchanged very long, although it may have been the most ancient fashion.