About the meaning of feasts
Saturday and New Moon
1) Saturday Shabbat שַׁבָּת
Saturday was described in Chapter 8.
2) New Moon Rosh Khodesh ראׁשׁ חדֶשׁ
Since the holidays are closely associated with the New Moon, according to our law the New Moon has the status of semi-feast. During the existence of the Temple of Jerusalem, the New Moon (the first day of each month) was celebrated by special worship, as it is written:
Also in the day of your gladness, and in your appointed seasons, and in your new moons, ye shall blow trumpets over your burnt-offerings, and over the sacrifices of your peace-offerings; and they shall be to you a memorial before your God: I am YHWH your God. (4M 10:10)
The first day of each month we consider a semi-feast, for this reason worship is longer on this day than on the common days.
During the New Moon we add a special prayer called עִנְיַן ראׁשׁ חדֶשׁ Inyan Rosh Khodesh.