It is the practice, as far as I know, of Orthodox Jewish men to put on phylacteries (tefillin), on their heads, while they pray in the morning. I wonder if the practice of the yarmulke is a reminder of that? Hmmm.
An Orthodox Jewish male 13 years or older wears tefillin on his head and arm every morning, except for on Shabbat and during certain special days and periods (which vary by custom). This commandment is derived from Exodus 13:9 and Deuteronomy 6:8:
And you shall bind them as a sign upon your arm, and they shall be as totafot between your eyes.
The meaning of the word totafot
is debated, but in most Orthodox Jewish translations of the Bible, I've seen it rendered as "a reminder."
Regarding the skullcap, Jews will admit that it is not a biblical commandment, nor even a rabbinical commandment. There are various "tales" as to how the custom of wearing the skullcap developed. The purpose of the skullcap seems to be to remind its wearer that there is always something "above them," i.e. God. When something has been a custom long enough, it becomes a de facto
rule for Orthodox practioners. Technically, you only need to wear the skullcap during prayer or when you're eating (since you need to say prayers before and after food).
Of course, I wonder if most jews wear headware? I would assume only the most pious do
And, if you see this very nice video of HIS ALL HOLINESS in a synagogue (shh don't remind anyone of the canons about this...) I do not see women with head coverings.
Almost all Orthodox Jewish men wear headware at all times, except when exposed to water (often showering or taking a dip in the ritual bath). Those who adhere to stricter authorities, such as most Hasidic groups, often wear a second piece of headgear when praying, to show that they are actually going through the extra step of covering their heads specifically for the act of prayer. This is why a lot of Jews can be seen wearing all sorts of hats (hint: they're wearing a skullcap under the hat).
Orthodox Jewish women must cover their hair once they marry. I have heard of some extremely strict Hasidic sects that encourage girls to cover their heads, but I've never seen it in practice. The requirements for covering are debatable, and there are many different types of headwraps, from a modest, thick cloth, to a flamboyant wig. The wigs, I still don't understand. The point of covering the head is to keep the hair, a sign of the woman's sexuality, private to her husband. But if you look just as "desirable," perhaps even moreso than they do in their natural hair, then what's the point?
To be honest, I'm still a little bothered by the idea of seeing little six year old girls covering their heads in Orthodox churches. I suppose I'm fine with it if they're doing it on their own, because maybe they want to be like their older sisters or mothers. But if their parents are making them... well, it's not my place to judge either way.
As an ex-Orthodox Jew, I would be happy to attempt to answer any other questions you might have about the customs.