The Hebrew calendar uses lunar months, which are based on the phases of the moon, e.g. the new moon is always the first day of the month, and months are always 29 or 30 days long. The Gregorian calendar’s months are fixed to the solar year, so the two never line up 1:1.
Since there aren’t a whole-number of lunar months in a solar year (or even a whole number of days in one lunar month) the Hebrew calendar adds a thirteenth leap month in seven out of every 19 years to keep it roughly in sync with the solar calendar. That’s why Rosh Hashana (or the first day of Tishrai) always falls between September 5 and October 5.
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