On the last day of Succot, we start to pray for rain, geshem. Geshem as linked to our ability to pray goes back to Genesis 2:5: “When no shrub of the field was yet on earth ... because the Lord God had not sent rain upon the earth.” Rashi explains that God did not send rain upon the earth until humanity sensed the world’s need for rain and prayed for it. God did not want it to rain until humanity “recognised the goodness of geshamim”.
Genesis uses the word matar for rain. Lehamtir means to shower something on someone, not necessarily rain, eg the manna which God showers on Israel in the desert. Mitriyah (umbrella) derives from matar.
The first big rain of the season is called the yoreh, the demonstrator. Ibn Ezra explains that we hope the yoreh will demonstrate the prospects of a good year ahead.
As a reward for fulfilling the commandments, God promises to send geshem b’ito, rain at the ideal time, which is at night. Gishmei berachah, rains of blessing, are the rains of Friday night, when we are all home enjoying the Shabbat meal.