From Rosh Ha Shannah (the Jewish New Year) to Yom Kippur (the Day of Atonement), a period known as the Days of Awe is a time of reckoning for observant Jews. During these ten days, Jews will seek to amend the failures and faults of the previous year. This period on the Jewish calendar is called the "Days of Awe", because it is a season of introspection, repentance, restitution (for sins against people), and Tashiach (the ceremony of collective casting of sins into a body water) in hopes that the scales will be tipped and another year secured. Jewish-New-Year cards often express the wish: "May your name be inscribed for another year!" This is an expression of hope that the requirements for that inscription will be met and that G-d (that's the Orthodox way of writing "God" in English) will make the inscription for the New Year. This inscription is made in the Book of Remembrance.

There's a discussion among the ancient rabbinical sages about the role of the Book of Remembrance, also called the Book of Life, during the Days of Awe. The discussion centers on the difference of interpretation between two dynasties of rabbinical authorities, the house of Shammai (Beth Shammai) and the house of Hillel (Beth Hillel). Here's the text of this discussion:

House of Hillel (Beth Hillel):

Three books are opened [in heaven] on New Year, one for the thoroughly wicked, one for the thoroughly righteous, and one for the intermediate. The thoroughly righteous are forthwith inscribed definitively in the Book of Life; the thoroughly wicked are forthwith inscribed definitively in the book of death; the doom of the intermediate is suspended from New Year till the Day of Atonement; if they deserve well, they are inscribed in the Book of Life, if they do not deserve well, they are inscribed in the book of death. Said R. Abin, What text tells us this?--- 'Let them be blotted out of the book of the living, and not be written with the righteous' (Psalm 69:28). 'Let them be blotted out from the book' --- this refers to the book of the wicked. 'Of life' --- this is the book of the righteous. 'And not be written with the righteous' --- this is the book of the intermediate. R. Nahman b. Isaac derives it from here: 'And if not, blot me, I pray thee, out of thy book which thou hast written,' (Exodus 32:32). 'Blot me, I pray thee' --- this is the book of the wicked. 'Out of thy book' --- this is the book of the righteous. 'Which thou has written' --- this is the book of the intermediate.¹

It has been taught: Beth Shammai say, There will be three groups at the Day of Judgment --- one of thoroughly righteous, one of thoroughly wicked, and one of intermediate. The thoroughly righteous will forthwith be inscribed definitively as entitled to everlasting life; the thoroughly wicked will forthwith be inscribed definitively as doomed to Gehinnom, as it says. 'And many of them that sleep in the dust of the earth shall awake, some to everlasting life and some to reproaches and everlasting abhorrence' (Daniel 12:2). The intermediate will go down to Gehinnom. ¹