Taanit, Chapter One, Mishnah Three
This mishnah teaches when we begin to ask for rain in the ninth blessing of the Amidah. We should note that at the very beginning of the rainy season we begin to mention rain but we do not yet ask for it. Later, when the rainy season should really begin in full force, we begin to ask for rain. In our prayers we slowly build up to really petitioning God for rain.
1) On the third of Marheshvan they [begin to] ask for rain.
2) Rabban Gamaliel says: on the seventh, fifteen days after the Festival [of Sukkot] so that the last of the Jews reaches the river Euphrates.
Section one: The third of Marheshvan (today called Heshvan), the second month of the year, is when we begin to ask for rain. This is when the rainy season is supposed to begin.
Section two: Rabban Gamaliel delays asking for rain until the seventh of Marheshvan, which gives pilgrims who were making their way back from Israel time to reach the river Euphrates in Babylonia. It would not be appropriate to begin to ask for rain while Jews were still returning from performing the important mitzvah of making a pilgrimage to the land of Israel and to the Temple in Jerusalem.