CHOL HAMOED

'Chol HaMoed', (חול המועד) a Hebrew phrase which means "weekdays [of] the festival", refers to the intermediate days of Passover and Sukkot. During Chol HaMoed the usual restrictions that apply to the Biblical Jewish holidays are relaxed, but not entirely eliminated.^[1] Hallel and Mussaf prayers must be said on these days, as on Yom Tov, although on Chol Hamoed of Passover, an abridged form of Hallel is recited. The tachanun prayer is also omitted.
Passover is a seven-day festival (eight in the Diaspora), of which days second though sixth - third though sixth in the Diaspora - are Chol HaMoed. Sukkot is a seven-day festival, of which days second though seventh (third through seventh in the Diaspora) are Chol HaMoed.
On Chol HaMoed, tefillin are not worn during the prayers by all except certain groups of Ashkenazi Jews and Yemenite Jews. Among those who do wear tefillin on Chol HaMoed, some omit the blessings and others recite the blessings, depending on one's ancestral custom. Even those who wear tefillin on Chol HaMoed remove the tefillin before Hallel, out of respect for the festive nature of Chol HaMoed, a festive nature which is especially palpable during the recitation of Hallel. The one exception to this practice is the first day of Chol HaMoed Pesach, when the Torah reading (which follows Hallel) discusses the mitzvah of tefillin. Because the Torah reading on that particular day especially focuses on the tefillin, those who wear tefillin on Chol HaMoed retain their tefillin during Hallel and only remove the tefillin after the Torah reading is completed and the Torah scroll has been returned to the Ark.
On Chol HaMoed there are four ''aliyot'' at the Torah reading in synagogue, as opposed to the standard three of weekdays, pointing to the festive nature of Chol HaMoed.

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References

1. ''Shulchan Aruch'' ''Orach Chayim'' 530