Why does a righty place his tefillin on his left arm, and a lefty on his right arm? It is based on a Pasuk in Parshat Bo, which states regarding the tefillin that "it shall be for a sign upon your arm (ידכה)" (Shemot13:16.) Rather than the usual spelling, ידך, the Torah uses this unusual spelling to allude to the fact that tefillin should be placed on יד כהה, the weak hand.
What is the significance of placing tefillin on our weaker arm? Rabbi Moshe Feinstein suggests that one's strong arm represents performing actions with strength and inner excitement, while one's weak arm represents doing things in a strained, burdensome fashion. When the Torah insists that we place Tefillin on our weak arm, it is symbolically demanding that we perform even the more difficult mitzvot with the same flair as if we were doing them with the strong arm. The Sefer HaChinuch famously writes that our feelings follow our actions. Often, when feeling weak in a certain area, by acting with more strength we can start to feel more strength.
Rabbi Michael Macks will be contributing weekly divrei torah as he is able