Tefillin have their origin in the Torah, the first five books of the Bible--occasionally referred to by Christians as the Old Testament. They exist in the context of several of God's laws (God being big on laws) outlining the relationship of a Jew with Him, capital 'h' there, and don't you forget it. The commandment of their origin can be found in the book of Exodus, with variations to be found in Deuteronomy:
'And you shall love the Lord your God with all your heart, with all your soul, and with all your being. Take these instructions which I command you this day, and follow them; so shall you consecrate yourselves to your God. Teach them faithfully to your children; recite them in your home and on your way, when you lie down and when you rise up. Inscribe them on the doorposts of your house, and on your gates. Bind them as a sign upon your hand and as a remembrance between your eyes.'
Strong words, and quite specific, especially given God's better known modus operandi of burning bushes and other mysterious ways. But Jews being people, and people being what they are, different interpretations developed. The Sadducees and the Karaites (medieval Jews!) didn't go in for the literal, and took the passage to mean that one should always be mindful of the Torah, as if it were ever in front of one's eyes. The somewhat less imaginative Pharisees, on the other hand, felt God's laws weren't really open to discussion, and so started producing Tefillin by the cartload.
The Tefillin are small black boxes (batim), in which are kept four sets of key biblical texts (parshiot) written on tiny scrolls. Each scroll is hand-written by a scribe in Israel, so you won't find any Tefillin makers in the diaspora who don't import their goods. If any mistakes are made, the scribe has to chuck the whole scroll and start over, so a nicely made set tends to run a few hundred dollars. They come two boxes to a set (unless you're a Cabalist, in which case you'll need four), and have black leather straps attached to them for binding purposes (retzu'ot). The arm-Tefillin strap is wrapped around the arm seven times--the weaker arm--leaving the box at heart level. The head-Tefillin rests on the forehead, about two fingers' worth above the eyes, and no lower. Upon your hand and between your eyes, check.
As to teaching it your children, strapping on Tefillin is the first mitzvah performed by a Jewish male upon his Bar Mitzvah. Boys are trained in putting them on a couple of months before their thirteenth Hebrew birthdays, in what to an outsider, unfortunately, has all the appearance of a bizarre, criminal bondage ceremony.
Among those that wear them, Tefillin are worn every weekday morning. The wearing of them is a mitzvah of great significance; even during the Holocaust (just couldn't get through a piece on Jews without mentioning it, could I?), Jews were known to have smuggled them into Nazi concentration camps so they could continue to worship.
The Text of the Parshiot:
Exodus, 13:1-10
'And the LORD spake unto Moses, saying, Sanctify unto me all the firstborn, whatsoever openeth the womb among the children of Israel, both of man and of beast: it is mine. And Moses said unto the people, Remember this day, in which ye came out from Egypt, out of the house of bondage; for by strength of hand the LORD brought you out from this place: there shall not leavened bread be eaten. This day came ye out in the month Abib. And it shall be when the LORD shall bring thee into the land of the Canaanites, and the Hittites, and the Amorites, and the Hivites, and the Jebusites, which he sware unto thy fathers to give thee, a land flowing with milk and honey, that thou shalt keep this service in this month. Seven days thou shalt eat unleavened bread, and in the seventh day shall be a feast to the LORD. Unleavened bread shall be eaten seven days; and there shall no leavened bread be seen with thee, neither shall there be leaven seen with thee in all thy quarters. And thou shalt shew thy son in that day, saying, This is done because of that which the LORD did unto me when I came forth out of Egypt. And it shall be for a sign unto thee upon thine hand, and for a memorial between thine eyes, that the LORD'S law may be in thy mouth: for with a strong hand hath the LORD brought thee out of Egypt. Thou shalt therefore keep this ordinance in his season from year to year.'
Exodus 13:11-16
'And it shall be when the LORD shall bring thee into the land of the Canaanites, as he sware unto thee and to thy fathers, and shall give it thee, That thou shalt set apart unto the LORD all that openeth the matrix, and every firstling that cometh of a beast which thou hast; the males shall be the LORD'S. And every firstling of an ass thou shalt redeem with a lamb; and if thou wilt not redeem it, then thou shalt break his neck: and all the firstborn of man among thy children shalt thou redeem. And it shall be when thy son asketh thee in time to come, saying, What is this? that thou shalt say unto him, By strength of hand the LORD brought us out from Egypt, from the house of bondage: And it came to pass, when Pharaoh would hardly let us go, that the LORD slew all the firstborn in the land of Egypt, both the firstborn of man, and the firstborn of beast: therefore I sacrifice to the LORD all that openeth the matrix, being males; but all the firstborn of my children I redeem. And it shall be for a token upon thine hand, and for frontlets between thine eyes: for by strength of hand the LORD brought us forth out of Egypt'.
Deuteronomy 6:4-9
'Hear, O Israel: The LORD is our God , the LORD is one: And thou shalt love the LORD thy God with all thine heart, and with all thy soul, and with all thy might. And these words, which I command thee this day, shall be in thine heart: And thou shalt teach them diligently unto thy children, and shalt talk of them when thou sittest in thine house, and when thou walkest by the way, and when thou liest down, and when thou risest up. And thou shalt bind them for a sign upon thine hand, and they shall be as frontlets between thine eyes. And thou shalt write them upon the posts of thy house, and on thy gates.'
Deuteronomy 11:13-21
'And it shall come to pass, if ye shall hearken diligently unto my commandments which I command you this day, to love the LORD your God, and to serve him with all your heart and with all your soul, That I will give you the rain of your land in his due season, the first rain and the latter rain, that thou mayest gather in thy corn, and thy wine, and thine oil. And I will send grass in thy fields for thy cattle, that thou mayest eat and be full. Take heed to yourselves, that your heart be not deceived, and ye turn aside, and serve other gods, and worship them; And then the LORD'S wrath be kindled against you, and he shut up the heaven, that there be no rain, and that the land yield not her fruit; and lest ye perish quickly from off the good land which the LORD giveth you Therefore shall ye lay up these my words in your heart and in your soul, and bind them for a sign upon your hand, that they may be as frontlets between your eyes. And ye shall teach them your children, speaking of them when thou sittest in thine house, and when thou walkest by the way, when thou liest down, and when thou risest up. And thou shalt write them upon the door posts of thine house, and upon thy gates: That your days may be multiplied, and the days of your children, in the land which the LORD sware unto your fathers to give them, as the days of heaven upon the earth.'
(The above selections are taken from the King James Bible.)