Why is Rosh Chodesh observed on two days in some months and only one day in others?

There are a number of things that you need to understand that go into answering your question.

In Israel, the "Head of the Month" for every month is one day. It was argued Talmudically that if one could hear the shofar blow on the new moon, one would know when the month has begun. It did not matter that there were several competing factions that withheld the beginning of the month during spats AND that the calendar was understood by all AND that folk could just look up.

It was also argued that in the Diaspora, it was felt that folk might get mixed up on the timing of the shofar having been sounded because they were literally out of the area. (Same issue with the calendar and the ability to look up). This is why most Holidays are drug into two days of celebration or elongated outside of Israel.

Toss in that certain Holidays (Shabbats) take precedence over the opening of a month. The prohibition of begin and ending jobs on the Sabbath is the reason for this.

Rosh Chodesh was traditionally celebrated at the very beginning of the New Moon when the very first sliver of a new crescent was spotted. Since solar months are longer than lunar ones, we will have 2 New Moons every so often because lunar months are about 28 days and solar ones 30-ish. So every once in a while there will be 2 new moons.

Rosh chodesh means head of the month. Since the Hebrew Calendar is a lunar calendar, there can only be one "head of the month." Could you be thinking of the Christian calendar when there can sometimes be two new moons during a single month?

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