Why is the tefillin strap wrapped around the arm seven times?

The connection between the arm tefillin and the number seven is explained in various ways:

• Tefillin are a symbol of the loving relationship between the Jewish nation and G‑d, which is analogous to the relationship between a husband and wife. Seven blessings are recited at a wedding ceremony, and the tefillin are correspondingly wrapped seven times.1
• The seven coils of the arm tefillin correspond to the seven words in the verse2 "Poteach et yadecha u'masbia le'chol chai ratzon" – "You open Your hand and satisfy every living thing [with] its desire."
• The purpose of tefillin is to bind our mind and emotions to G‑d. The mind is represented by the tefillin of the head, and the emotions are represented by the positioning of the arm tefillin near our hearts, the seat of emotion. Devoting our emotions to G‑d -- i.e. developing a love and awe for the Creator -- impacts our behavior, thus the emotive tefillin are placed on the arm, which is symbolic of action.
  According to Kabbalah, there are seven primary emotions (see The Sefirot). Since the arm Tefillin represents the channeling of our emotions toward G‑d, we therefore wrap the straps seven times around our arm, representing the seven emotions.

All the best,

Rabbi Baruch S. Davidson