() החדש הזה לכם. היינו כח לחדש יהיה לכם שתוכלו לחדש הן בדברי תורה והן בהנהגה, נותן השי"ת זה הכח לישראל.
That is to say, the power/energy of the month will be for you, that you should be able to renew yourselves with torah and in your actions. Hashem gives bnei yisrael this strength /power/energy.
On a personal and national level, Rosh Chodesh is a time of renewal and revival.
Rabbi Shimshon Raphael Hirsch Commentary on Torah (Ex:12:2)
This renewal is to be to you a beginning of New moons (literally a beginning of renewals, of revivals)"
...Each time the moon finds the sun again, each time it receives its rays of light afresh, God wants the Jewish people to find God again and to be illuminated with fresh rays of God's light, wherever, and however, in running their course, they have had to pass through periods of darkness and obscurity. (pg. 125)
What is the reason that women refrain from strenuous labor on Rosh Chodesh?
Pirkei d' R. Elizer
When the men came to take their wives' gold earrings for the golden calf, the women refused to hand them over. They told their husbands, "We will not obey you and help you make an abomination that has no power or salvation." God rewarded them in this world [for this refusal] by granting them a greater degree of observance on Rosh Chodesh. And God rewards them in the World to Come by giving them the power of constant renewal which characterizes Rosh Chodesh.
(Book of our Heritage, Eliyahu Ki Tov, pg. 222)