The Talmud in Menachos 36a derives from this pasuk that one should first put the tefillin shel yad on the arm, then the tefillin shel rosh on the head. When he removes the tefillin he should first remove the shel rosh. For, when the shel rosh is on his head, he should be wearing both tefillin. There are a number of reasons for this halacha.
The Chezkuni suggests a novel pedagogic approach. Before one can make an external sign, before he can promulgate his ideas and beliefs, he must initially concretize the beliefs in his own mind. They must become an integral part of his personality. In order to successfully teach and inspire others, it is necessary to maintain their respect. It is hypocritical to try to impress others while one is himself deficient in this specific area. Such a teacher will only undermine his own goals. This is the rationale behind the requirement for having the tefillin on the arm while the tefillin are on the head.
Horav Chaim Elazary z.t.l. suggests another reason for this requirement. The two tefillin symbolize activity and thought. The shel yad, obviously, represents movement and activity, while the shel rosh signifies thought and contemplation. Both of these functions are essential to serve Hashem. Action, however, takes priority. This is consistent with Bnei Yisrael’s acceptance of the Torah on Har Sinai. “Naase V’nishmah. We will do and we will listen!” they exclaimed. Action in mitzvos is paramount; intellectual appreciation will follow.
Indeed, it is only through mitzvah performance that one truly begins to appreciate the profound rationale behind mitzvos. The shel rosh without the shel yad is inappropriate. To delve into taamei ha’mitzvos, reasons for the mitzvos, without actually performing them will result in the development of an intellectual apostate.