Answer:
   
   They are called "tefillin" (mentioned in the Torah as "totafos", and
   often seen in English translations as "frontlets"). They contain
   parchments with verses from the Torah. During the weekday morning
   service, one of the boxes (the "Hand t'filluh") is placed upon the
   left arm so that it rests against the heart, and the suspended leather
   strap is wound around the left hand, and around the middle finger of
   that hand. The other box (the "Head t'filluh") is placed upon the
   head, above the forehead, so as to rest upon the cerebrum. This is in
   fulfillment of the Torah commandments. If you go to a traditional shul
   and lack tefillin, you can be sure that someone will lend you his and
   assist you in fulfilling this mitzvah.
   
   Note that the actual commandment is to wear them anytime, all the
   time. That is, anytime a day for a moment to fullfill the obligation,
   and all the time to fullfill the non-obligatory commandment. The
   rabbis forbade wearing them at nightime (except under very specific
   circumstances) so they must be worn during the day only.
   Traditionally, we consider wearing them for prayers important, though
   that should not be confused with the actual commandment. Hence, their
   primary use during services.
   
   The two boxes each contain four sections of the Torah inscribed on
   parchment. These passages cite:
    1. The Shema (Deuteronomy 6:4-9) - pronouncing the Unity of The One
       G-d.
    2. Vehayah (Deuteronomy 11:13-21) - expressing G-d's assurance to us
       of reward that will follow our observance of the Torah's precepts,
       and warning of retribution for disobedience to them.
    3. Kadesh (Exodus 13:1-10) - the duty of the Jewish people to always
       remember the redemption from Egyptian bondage.
    4. Vehayah (Exodus 13:11-6) - the obligation of every Jew to inform
       his children on these matters.
       
   A good summary of the laws and customs regarding Tefillin may be found
   at [5]http://www.ahavat-israel.com/ahavat/torat/tefillin.asp.
   
   One of the medieval blood libels was to tell gentile peasants that
   Jews poisoned wells, and received coded magic instructions in small
   black boxes. The mobs would destroy the expensive tefillin to open
   them, and mistake the Hebrew verses as "magic codes," followed by the
   usual rape, murder, and pillage of Jews that (alas) characterized much
   of medieval Europe.
   
   Note that in some congregations, women also wear tefillin. Although
   halakha exempts women from this mitzvah, it does not explicitly
   prohibit them from following it. Some segments of Orthodoxy do feel
   that actions that are not commanded must be considered as forbidden.
   Others feel that people should not take on additional responsibilities
   until they fully carry out those actions that are commanded. Thus,
   while women such as Bruria (Rabbi Meir's wife) or Rashi's daughters
   may have been on a high enough level, women nowadays are not on a
   level that would allow them to wear tefillin.
   
   However, non-Orthodox movements, and some liberal segments of the
   Orthodox community, do permit it. In those movements that permit the
   practice, the wearing of teffilin has become an important way for
   Jewish women to express their Judaism.