The uniqueness of the Jewish head covering is implied in the blessing we recite each morning, when we thank Gd for "crowned Israel with splendor" (Talmud, Berachot 60b).
Many wonder on the need to cover the head. At home, in the street, at work… some answers…

The Talmud teaches us that the purpose of wearing the kippah is to remind us that Gd is the Supreme Authority “over above us" (Kiddushin 31a). Since our actions generally arouse an inner awakening, placing "something" tangible and symbolic above our heads can reinforce the idea that Gd is constantly watching us. The kippah is therefore a means of expressing our deep sense of respect for Gd. As long as we are in the synagogue or sitting at the Shabbat table, it is easy for us to think of Gd. But ideally, awareness of our Jewish identity should dominate every aspect of our lives: our relationships with others, the way we conduct our business, our worldview. It is therefore significant that the Yiddish word for headgear "yarmulke", comes from the Aramaic "yira malka" which means "fear of the King".
In Hebrew, the headgear is called "kippah", literally “dome”.

Be assertive

Wearing the kippah is a way of saying "I am proud to be a Jew". Interestingly, when non-observant Jews travel to Israel, they often wear kippah for the duration of their stay. This may stem from the feeling that the entire Land of Israel has the same degree of holiness as a synagogue. Or the disappearance of this embarrassment that often accompanies the public expression of our Jewishness in the Diaspora.
Wearing the kippah is also a major affirmation because it obliges the wearer to adopt a certain level driving. A person must then think twice before passing in line at the bank, or scolding an incompetent waiter.
Wearing the kippah makes us ambassadors of the Torah and has an impact on everyone else Jews.
The actions of a man wearing the kippah can create kiddush Hashem (sanctification of the divine Name) or conversely a chillul Hashem (desecration of His name). Of course, putting on a kippah does not automatically give us “role model” status. Unfortunately, we sometimes hear that a cultivator has committed certain wrongdoings.

When to wear a kippah

From a biblical point of view, only kohanim (priests), serving in the Temple, had to cover their heads (see Exodus 28: 4) However, for several centuries, it has been the custom that Jewish men wear a kippah in all circumstances, as the Code of Jewish Law states: “It is forbidden to walk 4 cubits without covering the head. »
Should you wear a kippah when playing sports? This question has been raised recently with all the publicity surrounding Tamir Goodman, an observant Jewish basketball player who is currently causing a stir in the United States. The answer is that it is better to wear a kippah, even a small one, hanging from your hair. (Velcro straps are very effective!) If this is not possible, due to conditions or game rules, it is acceptable to play without a kippah. When swimming or taking a bath, one should not wear a kippah. However, a head covering is obligatory when praying or studying Torah.
What kind of head covering should be used?
In general, anything is acceptable, from a baseball cap to a scarf tied over the head.
Of course, inside a synagogue, it is more respectful to use a simple kippah.

How big should she be?

According to Rav Moshe Feinstein, the minimum measurement is "anything that can be called headgear". According to Rav Ovadia Yossef, the kippah should be wide enough to be visible from all sides.
The style of kippah one wears is indicative of an interesting sociological phenomenon, it often denotes a person's affiliation to a certain group.
Thus, Yeshivist-style Jews wear a black velvet kippah. Zionist Jews often wear a colored crocheted kippah.
Many Chassidic Jews wear a fur hat (shtreimel or spodik) on Shabbat and holidays. Furthermore, many men also wear a hat during prayer to increase their awareness of the presence of the Almighty when they stand before Him (Mishna Berura 183:11).

The kippah at work

What happens if wearing a kippah conflicts with practicing a job or our chances of promotion?
Rav Moshe Feinstein writes that in some cases it is possible to be lax. For example, a lawyer may not serve his client properly if the juror is distracted by his kippah. US Senator Joe Lieberman may be using similar reasoning. This can of course work both ways.
An influential businessman once told me that for every customer he "lost" because of his kippah, he gained two who lived up to that statement. for his integrity and courage in wearing the kippah.
A story relates that Rabbi Levi Yitzchak of Berdichev once saw a man running. He called out to her: "Where will you run to?" "I'm going to work," replied the man.
"But maybe your livelihood is just in the other direction and you're drifting away from it!" retorted the Rebbe

Source: Shraga SIMMONS