Tefillin are a Mitzvah.

The word Mitzvah means commandment. It also means connection. Through fulfilling a Divine commandment we become connected with the Divine.

An ideal relationship between two entities is when each party is in it for the benefit of the other. A focus on the other, forms the strongest connection with it. In every Mitzvah there are thus two aspects: 1) G-d loves us, so He gives us a commandment. 2) We love G-d, so we fulfill it.

So what is the significance of Tefillin? It depends from whose perspective: G-d's or ours.

Wedding Band

Regarding Tefillin G-d writes in His Torah¹ "and you shall bind them a sign upon your arms and they shall be for a reminder between your eyes".

Love is a very powerful attribute. Your every decision and thought is molded by your concern for your beloved. Yet love per se is very abstract and cannot be quantified or displayed. So we have signs of our love, such as a wedding band. A wedding band is essentially just a piece of gold. Anyone can buy it, and anyone can wear it. But society designated the wedding band as a sign of a deeply rooted committed love. It is no longer a gold ring. It is a wedding band.

G-d is aware that mortal beings would not always be cognizant of this abstract love, so He gave the Jew Tefillin as a tangible sign of His eternal love.

Wherever a Jew may be - geographically, historically, emotionally, or spiritually - he wears the Tefillin like a newlywed bride wears her wedding band. Perhaps to some extent Tefillin are leather boxes and straps, but in the context of a loving relationship they are a sign of a Divine bond.

It's Not Me, It's You

In most prayer books there is a meditation illustrating what the Jew thinks about when he dons Tefillin. He thinks about the oneness of G-d. He thinks about the Exodus from Egypt; the countless miracles G-d did for us as a People, and for me as a person.

He thinks if someone saved my life I would be forever indebted and grateful to that individual. He thinks G-d gave me life and sustains it constantly; I ought to spend my entire life giving to G-d.

So he takes a moment every (weekday²) morning to unite his intellect, emotions, speech and actions in a gesture of thanks to G-d. He dons (action) Tefillin on his bicep parallel to his heart (emotions), on his head above his brain (intellect), and recites blessings and prayers (speech).

Thus the Jews says: G-d this might just be a brief moment in my day, but it is an all encompassing moment at the beginning of my day. It synchronizes all of my faculties for the rest of the day. It aligns my thoughts, feelings, words and deeds, in Your direction.

See also How do I put on Tefillin?