The 10-day period beginning on Rosh Hashanah and ending on Yom Kippur is known as the "Ten Days of Repentance"; this is the period, say the sages, of which the prophet speaks when he proclaims (Isaiah 55:6) "Seek G-d when He is to be found; call on Him when He is near." It is thus a most auspicious time to rectify the failings and missed opportunities of the past and positively influence the coming year. Psalm 130 and other special inserts and additions are included in our daily prayers during these days.
The Shabbat between Rosh Hashanah and Yom Kippur is called Shabbat Shuvah, "Shabbat of Return."
The name derives from the Haftarah (reading from the
prophets) for this Shabbat, which opens with the words (Hosea 14:2),
"Return O Israel unto the L-rd your G-d..." According to master Kabbalist Rabbi Isaac Luria ("Ari"), the seven days between Rosh Hashanah and Yom Kippur (which will always include one Sunday, one Monday, etc.) correspond to the seven days of the week. The Sunday between Rosh Hashanah and Yom Kippur includes within itself all Sundays of the year; the Monday embodies all Mondays, and so on. Shabbat Shuvah is thus the archetypal Shabbat -- the juncture in time at which we are empowered to influence every Shabbat of our year.