The Shabbat between Rosh Hashanah and Yom Kippur is called Shabbat Shuvah, Shabbat of Return because its special haftarah reading begins with the words Shuvah Yisrael "Return O Israel", from the prophecy of Hoshea. It is also referred to as Shabbat Shuvah because it falls during the Ten Days of Repentance.
The prayer service on this Shabbat is the same as on an ordinary Shabbat with the exception of the additions that are made to the Amidah throughout the Ten Days of Repentance. Avinu Malkenu is not recited. In the blessing at the end of the Magen Avot prayer following evening services on Friday night, the words ha-Melech ha-Kadosh are substituted for ha-El ha-Kadosh toward repentance. Our Sages have said that when the wise address the people, G-d forgives the sins of Israel.
The Shabbat was given to Israel as a time for Torah study and prayer, and, although one should always take care not to pass the time idly or in inappropriate conversation, on Shabbat Shuvah one should be especially careful to concentrate entirely on Torah, prayer, and reflection on repentance, thereby attaining forgiveness for whatever unfitting behavior may have marred other Sabbaths.