שולחן ערוך אורח חיים · סימן ל״א

English

It is prohibited to wear tefillin on Shabbos or Yom Tov since they are an אות (a sign) and if one were to also wear an extra sign it would be a disgrace to their sign.

English

...On Chol HaMoed it is prohibited to wear tefillin for the same reason, namely that Chol HaMoed is also an אות (sign). Rema: There are those who maintain that one is obligated to wear tefillin on Chol HaMoed [Beit Yosef quoting the Rosh] and the custom in all these regions is to put on tefillin with a beracha. The only difference is that the beracha is not recited out loud in shul as is normally done.