What is the reason for wearing tefilin?
is it to induce a person to study torah? Or perhaps in order to remember the exodus from Egypt?
If so, what is the connection between this to wearing black leather boxes with straps hanging down?
The physical properties of the tefillin are distinctly not described in the Torah. This fact is sometimes used to discuss the validity and usefulness of oral tradition.
This source sums it up pretty nicely:
As Rabbi Aryeh Kaplan describes in his book, "Tefillin" (NCSY 1973):
"There is no description of Tefillin (in the Torah), nor any hints as to how they must be made. The Torah merely outlines their contents and tells us nothing more...
...The Talmud itself cites Tefillin as a prime example of a case where the full description of the commandment is found only in the Oral Torah. If you think about it, you will realize that it was not necessary to write a description of Tefillin in the Torah. One need simply look at an older pair. Tefillin were worn by virtually every adult male throughout Jewish history, and they themselves provided as permanent a record as any book."
There are also a few discussions on this topic at chabad.org. Including this on the types of hide that may be used for the parchment:
And it is a halachah from Moses at Sinai that tefillin are tied round with their hair and sewn with their tendons.
The reason for tefillin looking the way they do is because G-d described them to Moses on Mt. Sinai.
The reason for wearing t'fillin comes from the first paragraph of the Shema
וּקְשַׁרְתָּם לְאוֹת | עַל-יָדֶךָ, וְהָיוּ לְטֹטָפֹת בֵּין | עֵינֶיךָ
And you should tie them as a sign onto your hand, and they should be a reminder between your eyes.
And also from the second paragraph of the Shema
וּקְשַׁרְתֶּם | אֹתָם לְאוֹת | עַל-יֶדְכֶם, וְהָיוּ לְטוֹטָפֹת בֵּין | עֵינֵיכֶם
(Basically same translation as above)
The gemarra Sanhedrin 88b and in other places discusses the form of Tefillin, explaining what the Torah means when it says to tie them to your hand and between your eyes.
...bear in mind that G-d commanded us to write on the parchment contained in the tefillin the four specific Biblical passages...which mention His unity and the Exodus from Egypt, in order that we remember the miracles and wonders He performed for us. They indicate His unity and omnipotence. He has enjoined us to place the arm tefillin adjacent to the heart, and the head tefillin over the brain, so that we submit our soul which is in the brain, as well as the desires and thoughts of our heart, to His service. Thus, by putting on the tefillin, one will be mindful of the Creator and restrict his pleasures.