A more direct answer to your question is that in the Torah (bible) it says:
...In the seventh month, on the first of the month, there shall be a sabbath for you, a remembrance with shofar blasts, a holy convocation. -Leviticus 16:24
Rosh Hashanah occurs on the first and second days of Tishri. In Hebrew, Rosh Hashanah means, literally, "head of the year" or "first of the year." Rosh Hashanah is commonly known as the Jewish New Year.
The first month of the Jewish calendar is Nissan, occurring in March and April. Why, then, does the Jewish "new year" occur in Tishri, the seventh month?
Judaism has several different "new years," a concept which may seem strange at first, but think of it this way: the American "new year" starts in January, but the new "school year" starts in September, and many businesses have "fiscal years" that start at various times of the year. In Judaism, Nissan 1 is the new year for the purpose of counting the reign of kings and months on the calendar, Elul 1 (in August) is the new year for the tithing of animals, Shevat 15 (in February) is the new year for trees (determining when first fruits can be eaten, etc.), and Tishri 1 (Rosh Hashanah) is the new year for years (when we increase the year number. Sabbatical and Jubilee years begin at this time).
For more info see: http://www.jewfaq.org/holiday2.htm