תפילין של יד ותפילין של ראש

The arm tefillin are hidden and the head tefillin are exposed. Chazal say in pirkei avos that one should not serve Hashem in order to receive reward [but out of love]. They add that the fear of Hashem should be upon us. We see that even after one serves Hashem from love, it is still necessary to have fear.

The explanation is that with what relates to our soul we must reach complete love and dveykus to Hashem. However the somewhat muddy body [הגוף העכור] cannot cling to Hashem. The body must have a deathly fear and be excessively vigilant that it doesn't express an opinion with respect to spiritual matters. It emerges that dveykus is from the soul and fear from the body. Therefore, the soul can reach the most elevated levels of love of Hashem provided that the body doesn't get involved and experiences fear that it shouldn't impede the love of the soul. The less body, the more love.

That is what the tefillin are about. The arm tefillin expresses our connection to Hashem and that is why it says וקשרתם לאות על ידך you should BIND it to your arm as a sign. Since our connection is in our pnimiyus, our internal world, therefore the tefillin are hidden. The head tefillin express our more physical bodily side, where we should always experience fear so that the shadow of holiness should always hover over us. That is why it is exposed.

First we lay the arm tefillin and only then the head tefillin, meaning that first and foremost we should connect to Hashem in the deepest and most pnimiyus'dike way and that will bring us to purify our bodies.

[Rav Yaakov Moshe Charlap ztz"l Mei Marom vol. 13 page 24]

Ps - The sfarim hakdoshim say that just as women get credit for the learning of their husbands and children, the same applies to the mitzva of wearing tefillin. So while women are sleeping comfortably in their beds or are preparing food for the children to take to school it is as if they are wearing tefillin. Hashem doesn't discriminate.