The symbolic book mentioned in Rosh Hashanah prayers as holding the names of those destined for life is the Book of Life.
In Jewish tradition, Rosh Hashanah is a day of divine judgment. The Talmud describes three heavenly books being opened: one for the completely righteous, one for the completely wicked, and one for people in between. The righteous are inscribed for life, while the intermediate judgment remains open until Yom Kippur.
This idea appears in High Holy Day liturgy and helps explain the traditional greeting “May you be inscribed for a good year.” The phrase does not mean that Rosh Hashanah is simply a birthday celebration; it also marks a period of repentance, prayer, and moral self-examination.
A common mix-up is with the Book of Jubilees or the Book of Esther. Those are named Jewish or biblical works, whereas the Book of Life is a theological record associated with divine judgment. The expression also appears in the Hebrew Bible and later Christian writings, though its Rosh Hashanah meaning is especially prominent in Jewish tradition.