Rosh Chodesh includes all the days of the month:
The day of Rosh Chodesh includes all the days of that month, similar to that Rosh Hashanah includes all the days of the year. This means to say that just as on Rosh Hashanah the Divine light which supplies blessing for the entire year is drawn down, similarly on Rosh Chodesh, the Divine light that supplies blessing for the entire month is drawn down. It is for this reason that Rosh Chodesh is called “Rosh” which means the head and not simply “Hatchala” which means the start, as just as the head includes all the life-force of the body, similarly Rosh Chodesh incorporates all of the Divine vitality of the days of that month.
The Divine light received on Rosh Chodesh versus Shabbos and the weekday:
Although Rosh Chodesh is not forbidden in Melacha, nevertheless it is also not considered by the verse one of the six days of work. We find this regarding the gates of the Heichal, in which during the six weekdays the gates were closed while on Shabbos and Rosh Chodesh the gates were open. This represents a special Divine light that Rosh Chodesh receives in contrast to the weekdays. During the week, the ray of Chochmah must pass through the Middos in order to reach its destination in Malchus. However, on Rosh Chodesh, the ray of Chochmah travels directly to Malchus without any mediums in between. Shabbos however is of even a higher level, as on Shabbos the level of Malchus is elevated to Chochmah, and does not need to receive from it.
The level of world which Rosh Chodesh corresponds:
The regular weekday corresponds to the world of Assiyah, the world of action. Rosh Chodesh corresponds to the world of Yetzira or Beriya. Shabbos corresponds to the world of Atzilus.
One is required to honor and respect Rosh Chodesh [with a festive meal] just as one would be required to do so for any Holiday, as on Rosh Chodesh there is an extra radiance of the soul. The Zohar states that on this day the Jew has an extra soul just like on Shabbos.
On Rosh Chodesh the fire of Gehinnom is extinguished similar to Shabbos. In this aspect the day of Rosh Chodesh is even higher than Yom Tov, as on Yom Tov the fire of Gehinnom remains. The reason for this is because both Shabbos and Rosh Chodesh were given to the Jewish people from the beginning of creation, while the Holidays were given as a result of the miracles.
 Sichas Chayeh Sara Mevarchim Hachodesh Kisleiv 1951; Vayeshev Mevarchim Hachodesh Teves 1951; See Mamar “Lehavin Inyan Erev Rosh Chodesh” said on Parshas Toldos 5714
 Likkutei Torah Vezos Haberacha 96; See also Derech Mitzvosecha Mitzvas Kiddush Hachodesh
 Or Hatorah Bereishis 22a; Sichas Chayeh Sara Mevarchim Hachodesh Kisleiv 1951
 Or Tzaddikim 31:1; Machazik Bracha 419:1; Kaf Hachaim 419:5
 See Zohar 81b; Tikkunei Zohar 421
 Mordechai Pesachim 166 in name of Pesikta; Birkeiy Yosef 419