Birkhot Keri’at Shema are unlike other birkhot ha-mitzvot instituted as preparation mitzvot, which contain the formula “asher kideshanu be-mitzvotav ve-tzivanu…” (Who has sanctified us with His mitzvot and commanded us…”). Rather, they are formulated as praise, thanksgiving, and some petition, and their purpose is to express more expansively the themes of Shema, whose essence is the first verse.
In the Shema we say “Hashem Eĥad” (“God is One”), denoting that He is the single entity that brings the world into being and sustains it and that there is none other than Him. In the first berakha of Keri’at Shema, we expand on this principle, and by praising Him for the light that is renewed daily, we continue to extol God, “Who constantly renews the work of Creation every day.” To emphasize His oneness, we praise Him as Creator of both light and darkness. At night, in the corresponding berakha, we praise him as “Ma’ariv aravim” (“the One Who brings on evening”) and add that He is “Borei yom va-laila” (“the Creator of day and night”). Hence, the principle of belief in God’s unity that appears in Shema is amplified in the first berakha.
The significance of the opening words, “Shema Yisrael,” is that the belief in God’s unity is revealed to the world through the Jewish people, who were put in the world for that purpose. This idea is amplified in the second berakha, in which we thank God for loving us and for giving us the Torah out of love. We pray for the opportunity to understand the Torah and fulfilling it with love, thereby revealing God’s name in the world.
“Hashem Elokeinu” (“Lord our God”) means that God is omnipotent and rules the world according to His will. His control of the world, with all its forces and components, was revealed most clearly in the Exodus, which is mentioned at the end of the third paragraph of Shema. In the third berakha we expand on this further and praise God, “You are the first and You are the last, and aside from You we have no king, redeemer, or savior. You redeemed us from Egypt…” We also mention the slaying of the Egyptian firstborns and the splitting of the sea. We conclude, “Blessed are You, Lord, Who redeemed Israel” (“Ga’al Yisrael”).
We thus see that all three berakhot are a continuation and expansion of the principles of faith that are found in Shema.
Because these berakhot are unlike others which we recite before the performance of mitzvot, confusing their sequence does not prevent fulfillment of the mitzva. Although certainly le-khatĥila they must be recited in the order that the Sages ordained, be-di’avad, if one changed the order, she still fulfills the mitzva. Likewise, if she recited the berakhot without reciting Shema, or if she only recited one of the berakhot, she is credited for what she recited (Peninei Halakha: Prayer, ch. 16 n. 1).