There is nothing in the Law of Moses which requires Jewish men (other than the priests) to cover their heads when they pray. It would seem to be another custom invented by Rabbis. It does serve to show their lack of recognition of Paul’s explanation that the head of the man is (represents) Christ – the Messiah (who needs no covering for sin).
1 Corinthians 11:3 But I would have you know, that the head of every man is Christ; and the head of the woman is the man; and the head of Christ is God. 4 Every man praying or prophesying, having his head covered, dishonoureth his head.
Uncomprehendingly they publically demonstrate the national dishonouring of their Messiah. This will change when he returns to save them as a nation.
Zechariah 12:10 And I will pour upon the house of David, and upon the inhabitants of Jerusalem, the spirit of grace and of supplications: and they shall look upon me whom they have pierced, and they shall mourn for him, as one mourneth for his only son, and shall be in bitterness for him, as one that is in bitterness for his firstborn.
From here: http://www.jewfaq.org/signs.htm
Cover your head so that the fear of heaven may be upon you. -Talmud Shabbat 156b
R. Huna son of R. Joshua would not walk four cubits bareheaded, saying: The Shechinah [Divine Presence] is above my head. -Talmud Kiddushin 31a
R. Huna son of R. Joshua said: May I be rewarded for never walking four cubits bareheaded. -Talmud Shabbat 118b
The most commonly known and recognized piece of Jewish garb is actually the one with the least religious significance. The word yarmulke (usually, but not really correctly, pronounced yammica) is Yiddish. According to Leo Rosten's The Joys of Yiddish, it comes from a Tartar word meaning skullcap. According to some Orthodox and Chasidic rabbis I know, it comes from the Aramaic words "yerai malka" (fear of or respect for The King). The Hebrew word for this head covering is kippah (pronounced key-pah).
It is an ancient practice for Jews to cover their heads during prayer. This probably derives from the fact that in Eastern cultures, it is a sign of respect to cover the head (the custom in Western cultures is the opposite: it is a sign of respect to remove one's hat). Thus, by covering the head during prayer, one showed respect for G-d. In addition, in ancient Rome, servants were required to cover their heads while free men did not; thus, Jews covered their heads to show that they were servants of G-d. In medieval times, Jews covered their heads as a reminder that G-d is always above them.
Whatever the reason given, however, covering the head has always been regarded more as a custom rather than a commandment. Although it is a common pious practice to cover the head at all times, it is not religiously mandatory. For example, it is widely accepted that one may refrain from wearing a head covering at work if your employer requires it (for reasons of safety, uniformity, or to reduce distractions). You can take off your yarmulke for a job interview if you think it will hurt your chances of getting the job. There is an amusing article about this dilemma, The Kippah Debate, at Aish.com.
There is no special significance to the yarmulke as a specific type of head covering. Its light weight, compactness and discreteness make it a convenient choice of head gear. I am unaware of any connection between the yarmulke and the similar skullcap worn by the Pope.
It goes without saying that the Pope has no more understanding of Paul’s words than do the Jews.
I hope you have found this helpful.
May God bless you,