Covering one’s head, such as by wearing a kippah is described as “honoring God”

There is no explicit commandment for men to cover their heads, the practice of Jewish men doing so falls under a category of laws known as d’chukotai, basically when a custom is universally accepted and done by everyone it is treated the same as a law. Since Jewish men covering their heads has been an ancient practice and is discussed as being done in the Talmud ( a compilation of ancient teachings regarded as sacred and normative by Jews from the time it was compiled until modern times and is still regarded by traditional religious Jews) it fits into this category.

There is no explicit commandment for women either to cover their heads, there is however an explicit commandment for women to dress/behave modestly. It was customary for most women in the Ancient Near East, Mesopotamia and the Greco-Roman world to cover their hair when they went outside the home, they used veils and scarves. The unveiling of a woman’s hair was considered a humiliation and punishment (Isiah 3:17 Numbers 5:18) or the loosening of the hair of a woman suspected of adultery. Dressing modestly included a woman covering her hair and it is still a custom for women to cover their hair. The Jews see the requirement for a woman to cover her hair also from the passage about the Sotah– the woman warned by her husband to not be secluded with a specific man, who is subsequently in such a situation and is tested with the bitter waters ( in the Hebrew bible {the real bible} the ordeal of the bitter water was a Jewish trial by ordeal administered by a priest in the tabernacle to a wife whose husband suspected her of adultery, but the husband had no witnesses to make a formal case. It is described in the book of Numbers 5:11-31) to determine if she committed adultery or not. One of the steps is that her hair is revealed which indicates that there is an expectation (according to tradition) that a married woman should have all of her hair covered. The requirement does not apply to an unmarried woman HOWEVER, all women – old, young, married or single are required commanded by God to be modest.

According to the description of the priestly garb in Exodus 28:4,37,40 the high priest wore a miter (miznefet), and the ordinary priests a hat (migba’at). It was generally considered a sign of mourning to cover the head and face (II Samuel 15:30, 19:5 Jeremiah 14:3-4 Esther 6:12) In talmudic times, too men expressed their sense of grief while mourning by covering their heads.

CAN NON-JEWS COVER THEIR HEADS?

YES! In fact, if a non Jewish woman/man wishes to cover their hair as an expression of modesty and to acknowledge that God is above them (men) it is considered a very righteous thing to do. However, women who say that they are covering their heads for the sake of modesty must remember to dress modestly as well. Although head coverings are beautiful, they can’t just be worn to make a fashion statement, the entire outfit must be modest. Below is an example of being immodestly dressed with a head covering on:

In summary- Jewish tradition requires men to cover the head as a sign of humility before God, and women as evidence of modesty before men, although the bible does not explicitly command either men or women to cover the head. Now, there is nothing wrong for a non Jewish man or woman to cover their heads for the same reasons the religious Jews do.