The essence of life comes from prayer. Rabbi Nachman of Breslov derives this from a single verse: "Prayer to the God of my life" (Psalms 42:9). Prayer is not merely an appeal to the source of life. It is the channel through which life-force flows.
This is why a person should pray with every ounce of their strength, pouring all their energy into the letters of the prayers. When you do this, your energy is renewed. "They are renewed each morning; great is Your faith" (Lamentations 3:23). And faith is prayer, as we learn from Moses: "His hands were emunah (faith)" (Exodus 17:12), which the Targum renders "spread out in prayer."
Rabbi Nachman reveals that there are twelve versions of prayer, corresponding to the twelve tribes of Israel and the twelve constellations. Each tribe has its own gate in heaven through which its prayers enter. When a tribe prays, it arouses its corresponding constellation, and that constellation radiates downward, causing the vegetation and everything dependent on it to grow. "A star steps forth out of Jacob, and a tribe stands up out of Israel" (Numbers 24:17). "Stands up" refers to the standing prayer, the Amidah.
This is why the Talmud compares livelihood and marriage to the splitting of the Red Sea (Pesachim 118a; Sotah 2a). The sea split into twelve lanes for the twelve tribes (Pirkei DeRabbi Eliezer 42). Through prayer, the Jewish people bring about a union between the Holy One and His Shechinah. And in proportion to the union their prayer creates, they receive their livelihood and their marriage partner.
Clapping hands during prayer is part of this process. The physical act of clapping breaks through the barriers of judgment, the way the twelve lanes broke through the walls of the sea. The body itself becomes an instrument of prayer, and every clap sends ripples upward.