The Reform Machzor contains this reading as an alternative selection to the traditional Haftarah. What makes this unusual is that, traditionally, the Haftarah is a selection from the Prophetic reading. The book of Nehemiah is found in the third division of the Hebrew Bible called the Writings. The connection to the holiday is that the Haftarah describes a public reading of the Torah on the first day of Tishrei–the date on which Rosh Hashanah is observed. This English translation is reprinted with permission from Tanakh: The Holy Scriptures published by the Jewish Publication Society.
7:72. When the seventh month arrived–the Israelites being [settled] in their towns–
8:1. the entire people assembled as one man in the square before the Water Gate, and they asked Ezra the scribe to bring the scroll of the Teaching of Moses with which the LORD had charged Israel.
8:2. On the first day of the seventh month, Ezra the priest brought the Teaching before the congregation, men and women and all who could listen with understanding.
8:3. He read from it, facing the square before the Water Gate, from the first light until midday, to the men and the women and those who could understand; the ears of all the people were given to the scroll of the Teaching.
8:9. Nehemiah the Tirshatha, Ezra the priest and scribe, and the Levites who were explaining to the people said to all the people, "This day is holy to the LORD your God: you must not mourn or weep," for all the people were weeping as they listened to the words of the Teaching.
8:10. He further said to them, "Go, eat choice foods and drink sweet drinks and send portions to whoever has nothing prepared, for the day is holy to our Lord. Do not be sad, for your rejoicing in the LORD is the source of your strength."
8:11. The Levites were quieting the people, saying, "Hush, for the day is holy; do not be sad."
Pronounced: hahf-TOErah or hahf-TOE-ruh, Origin: Hebrew, a selection from one of the biblical books of the Prophets that is read in synagogue immediately following the Torah reading.
Pronounced: roshe hah-SHAH-nah, also roshe ha-shah-NAH, Origin: Hebrew, the Jewish new year.
Pronunced: TORE-uh, Origin: Hebrew, the Five Books of Moses.