Rain brings water to the world, allowing all plants, animals, and people to survive. Therefore, it is proper to praise God and pray to Him for beneficial rain. The Sages thus instituted two mentions of rain into the Amida, to be recited during the rainy season, between Sukkot and Pesaḥ. In the second berakha, on the theme of God’s might, the Sages ordained that we praise the omnipotent God by declaring that He “makes the wind blow and the rain fall” (“mashiv ha-ru’aḥ u-morid ha-geshem”). This invocation is called “hazkarat geshamim” (“the mention of rain”). In the ninth berakha, in which we petition God for sustenance and livelihood, we ask Him to bring down “benevolent dew and rain” during the winter months. This is called “she’elat geshamim” (“the request for rain”).
Sukkot marks the start of the rainy season, so it would have been reasonable to start mentioning and requesting rain already at the beginning of the festival. However, rain on Sukkot is seen as a bad omen, since we cannot fulfill the mitzva of sitting in the sukka in the rain. For this reason, the Sages delayed hazkarat geshamim until after Sukkot and ordained that we begin reciting “mashiv ha-ru’aḥ” at Musaf of Shemini Atzeret, when synagogue attendance is high and it is a good time to announce the beginning of hazkarat geshamim. Since not everyone comes to Ma’ariv, and it is forbidden to announce anything just prior to the Amida of Shaḥarit, so the announcement is made at Musaf (Beit Yosef and SA 114:1-2).
Along with starting hazkarat geshamim, at Musaf of Shemini Atzeret we also recite Tefilat Geshem, the prayer for rain, in which we ask God that all the upcoming year’s rain be beneficial. It is customary to open the ark for Tefilat Geshem and to recite it with great intent and supplication. Ashkenazic custom treats this prayer like the prayers of the Days of Awe; the ḥazan wears a kittel and chants a special melody, as on the Days of Awe.
The custom of Sephardim and some Ashkenazim is to recite Tefilat Geshem before Musaf, and the custom of most Ashkenazim is to insert it into the ḥazan’s repetition of the Amida, in the second berakha, at the point where hazkarat geshamim appears. For those who follow this custom, the gabbai must declare loudly, before the silent Amida: “Mashiv ha-ru’aḥ u-morid ha-geshem!” By virtue of this announcement, the congregants recite this phrase during their silent Amida, even though they have not yet recited Tefilat Geshem.
The Torah is likened to water: “Just as water gives life to the world, so the words of Torah give life to the world” (Sifrei, Ekev §48). Water animates the body and Torah animates the soul. Therefore, it is proper during Tefilat Geshem to have in mind spiritual water as well as physical water, so that the next year will be blessed with Torah.
It would make sense to begin she’elat geshamim with the first Ma’ariv after the festival. However, the Sages were concerned about pilgrims who traveled great distances, so they delayed the beginning of she’elat geshamim for another 15 days, until the night of the seventh of Marḥeshvan. This allowed the last of the pilgrims, who came from across the Euphrates, to return home without getting caught in a downpour (SA 117:1). In Eretz Yisrael, we continue this beautiful custom, which reminds us of Temple times, to this day. (Regarding the proper practice outside of Eretz Yisrael, see Peninei Halakha: Prayer 18:7.)
If one forgot to say “mashiv ha-ru’aḥ” in Musaf on Shemini Atzeret or anytime afterward, he need not repeat the Amida as long as he said “morid ha-tal” (“Who brings down dew”; this is the prevailing custom in Eretz Yisrael). If one forgot she’elat geshamim anytime after the seventh of Marḥeshvan, he should insert it into the berakha of Shome’a Tefila. If he forgot to say it there, he should return to the ninth berakha (where it is normally recited) and continue the Amida from there. If he finished the Amida before realizing his omission, he must repeat the entire Amida. (See Peninei Halakha: Prayer 18:4-5.)
In the Diaspora, where there are two days of Yom Tov, Tefilat Geshem is also recited on the first day (Shemini Atzeret), just as in Eretz Yisrael. On the second day (Simḥat Torah), the yearly cycle of reading the Torah is completed.