Different groups of people have created various calendars and ways to track annual cycles of time. The Jewish calendar is based on a lunar cycle. Each month starts with a new moon. Occasionally there is a "leap" month.
The Jewish calendar has several "New Years". One is the first day of the first month, like the western calendar. However, a more important New Year holiday is celebrated on the first day of the seventh month. This holiday is Rosh Hashana. A simple explanation is that it is the start of the religious year. The date of the year changes at Rosh Hashana instead of at the beginning of the first month.
Another way in which the Jewish calendar is different than the standard Gregorian or Western calendar is that days begin at sundown. When something must happen on a certain day, some customs require waiting until stars can be seen.
Months: Nisan, Iyar, Sivan, Tammuz, Av, Elul, Tishre], Cheshvan, Kislev, Tevet, Shevat, Adar.