Our Sages of the Medrash tell us how great is the power of prayer before G-d. In Medrash Rabba to Parashat Nitzavim we read: 

"Great is prayer before the Holy One, blessed be He. R. Elazar said: "Would you like to know the power of prayer? If it [the [prayer] does not accomplish all of [what the worshiper is requesting], it accomplishes half of it. [For instance,] Cain stood against his brother Abel and killed him, whereupon a [Divine] edict was issued: “You shall be itinerant [Heb.: na] and restless [nad] in the land” (B'reshit 4,12). 

"Immediately, Cain confessed his sin before G-d: "My iniquity is too great to bear” (verse 13). Cain said, "Master of the universe, You bear the entire world, but you cannot bear me? For [among Your attributes of mercy are]: “Bearing iniquity and overlooking transgression” (Micah 7,18) – [please therefore] pardon my iniquity, which is great.’ 

"Cain then found mercy before G-d, and the “itinerant” half of the edict was withdrawn, as is written: “[Cain] resided in the land of Nod” (B'reshit 4,16). [That is, he no longer had to wander; however, his place of residence was Nod, which represents the second half of the decree.] From here you learn that prayer is great before the Holy One, blessed be He.
"Likewise King Chizkiyahu: When the prophet said to him: “Instruct your household, as you will [now] die” (Yeshayahu 38,1), the king immediately "turned his face to the wall [and prayed to G-d]” (verse 2). G-d then said to him: “I have heard your prayer… behold, I am adding fifteen years to your days” (verse 5) [that is, he was not die right then, but rather 15 years later]. As is written: “He grants the wishes of those who fear Him, and He hears their cry and saves them” (Tehillim145,19)."

The Talmud in Tractate Taanit cites several stories regarding the efficacy of prayer. For instance, Rebbe once declared a public fast because there had been no rain, and although the people fasted, there continued to be no rain. A man named Ilfa arose to lead the prayers, and as soon as he said "G-d makes the wind blow," the wind started to blow, and when he said "G-d brings rain," rain began to fall. Rebbe asked him: "What do you do? What is the source of the strength of your prayers?" Ilfa answered, "I bring wine for Kiddush and Havdalah to my poor neighbors and I recite the blessings for them."

The Talmud further recounts that when Rav came to a place where there was a drought, he declared a fast, but rain did not fall. A man arose to lead the prayers, and the same thing as above happened. Rav asked him, "What do you do?" The man answered, "I teach children, and the children of the poor as if they were children of the rich; whoever cannot pay, I do not charge him. I also have fish pools, and if a pupil is too lazy to learn, I get him to learn by giving him some of my fish until he is appeased and is drawn to the studies." 

This is the high level of the righteous: "The righteous man decrees, and G-d fulfills," as is written, "You [one who prays to G-d] will decree, and it will be accomplished for you" (Iyov/Job 22,28). 

This strength is found not only among the righteous, but is also hidden within every Jew. For every man has some level, even if not a high one, of a tzaddik, as is written: "Your nation - all of them are tzaddikim" Yeshayahu 60,21), and their prayers are  accepted. 

Our teacher HaRav Kook said that it will yet be revealed in the world how great is the power of prayer of Israel, to the point that the entire world will come to the Jewish People to request this force, and that this is as is written: "For My house will be called a House of Prayer for all the peoples" (Yeshayahu 56,7). 

May G-d grant that our prayers be accepted before the Master of All, the G-d of Israel, and that this coming year be one of goodness, redemption, and salvation.

Translated by Hillel Fendel