From A Simple Jew...
The arm tefillin represent physical action while the head tefillin represent the intellect. By putting on the arm tefillin first we are reconfirming our complete faith and commitment to Torah. When we accepted the Torah on Sinai - we first said that we would fulfill the Torah then we would listen to what it involves and try to understand its meaning. So too by tefillin, we bind them upon our arm as a sign that we fulfill the mitzvah simply because we were commanded to, then we place the tefillin upon the seat of our intellect - to say that even though we may not (yet) fathom their meaning nevertheless, we place our complete trust in Hashem.
(Rabbi Shimshon Raphael Hirsch)
(Source post here.)