This month shall be for you the beginning of the months, it shall be for you the first of the months of the year. (Shemot 12:2)
Kiddush Haodesh (the sanctification of the new moon) was the very first commandment given to the Jewish nation as a whole, which suggests that this is a most significant misvah. A thousand years later it was one of only three commandments that the Greeks prohibited. The other two were Shabbat and Milah (circumcision). The fact that they saw fit to prohibit Kiddush Hahodesh together with those two commandments certainly implies it is a most central mitzvah, but what exactly is its significance?
Rosh Hodesh, the start of the new month, symbolizes renewal. Just as the moon disappears at the end of each month but returns and grows to fullness, so too the Jewish nation has the ability to rise up from oblivion and restore itself to past greatness. This essential characteristic of the Jews was first demonstrated in Egypt when the Jewish people had fallen to the 49th level of impurity, one level above spiritual extinction. They renewed themselves to such a degree that only seven weeks later they were able to stand at Mount Sinai, receive the Torah, and experience prophecy! It was this concept of renewal that the Greeks attempted to eliminate by ending the observance of Rosh Hodesh.
Everyone makes mistakes. The problem is that when a person feels guilty about what he has done wrong and sees himself as a failure, he may give up and lose the strength to keep trying to grow. In order to avoid this, he must recognize that although he has made a mistake he can always get back up, dust himself off and start again.