What is the significance of the white hair sticking out of the head Tefillin?

Nice observation; most people don't notice the little hair which slightly protrudes from the front of the head tefillin. It is actually the tip of the calf's tail hair wrapped around the parchment scrolls inside the box.

We wrap the scrolls with a calf's hair to remember the sin of the Golden Calf. The Golden Calf was the first sin of the Jewish people as a nation and every subsequent sin is an outgrowth of it. Worshipping the Golden Calf was an attempt to free ourselves of G‑d's sovereignty. Tefillin, on the other hand, are a symbol of G‑d's rule and remind us that we are His servants. The Zohar writes that we should therefore allow the hair to extend out of the tefillin as a visible reminder to keep ourselves from sinning.

Others suggest that the tefillin actually serve as a rectification the sin of the Golden Calf, and as such we allow the calf's hair to protrude—to demonstrate this connection.1

Yours truly,

Rabbi Menachem Posner