A Time For Repentance

At the turn of the year, the season when kings go out to battle, Yoavled out the army force and devastated the land of Ammon, and then besieged Rabbah, while David remained in Yerushalayim; Yoavreduced Rabbah and left it in ruins
I Chronicles 20:1 (The Israel Bible™)

vai-HEE l’-AYT t’-shu-VAT ha-sha-NAH l’-AYT TZAYT ha-m’-la-KHEEM va-yin-HAG yo-AV et KHAYL ha-tza-VA va-yash-KHAYT et E-retz b’-NAY a-MON va-ya-VO va-YA-tzar et ra-BAH v’-da-VEED yo-SHAYV bee-ru-sha-LA-im va-YAKH yo-AV et ra-BAH va-ye-her-SE-ha

A Time For Repentance
In the above verse, the beginning of the year is called teshuvat hashanah which literally means 'the turn of the year.' The Hebrew year is cyclical in nature, and the holidays are repeated at the same time each year. In a certain sense, the beginning of a new year is in fact a return to the same period in previous years. Furthermore, the Jewish New Year focuses on God's judgement and man's repentance. The word teshuva, which means 'return', also means 'repentance'. Hence, the expression teshuvat hashanah also refers to the time of year when we are obliged to repent.
As we find ourselves in the "ten days of repentance", between Rosh Hashanah and Yom Kippur (Day of Judgement), this is the time of year where the Children of Israel focus on repentance and returning to Hashem (God).