בָּרוּךְ אַתָּה ה' אֱ-לֹהֵינוּ מֶלֶךְ הָעוֹלָם, זוֹכֵר הַבְּרִית וְנֶאֱמַן בִּבְרִיתוֹ וְקַיָּם בְּמַאֲמָרוֹPraised are You, Lord our God, Ruler of the universe, who remembers and is faithful to His covenant and maintains His word.
The covenant to which this berakhah refers is the one that God makes with Noah in the wake of the flood in this week's parashah / Torah reading. The symbol of this covenant is the rainbow (Genesis 9:13), and as such, whenever we see a rainbow we recall God's promise never again to destroy all the living things on Earth.
What is especially striking about this covenant is that God realized that the flood has been a mistake, that the destruction wrought had been in vain, because humans (in particular) were quite likely to transgress again, and as if to prove God's point, Noah does so almost immediately. God expresses regret over the flood in Genesis 8:21:
וַיֹּ֨אמֶר יְהוָ֜ה אֶל־לִבּ֗וֹ לֹֽא־אֹ֠סִף לְקַלֵּ֨ל ע֤וֹד אֶת־הָֽאֲדָמָה֙ בַּֽעֲב֣וּר הָֽאָדָ֔ם כִּ֠י יֵ֣צֶר לֵ֧ב הָֽאָדָ֛ם רַ֖ע מִנְּעֻרָ֑יו וְלֹֽא־אֹסִ֥ף ע֛וֹד לְהַכּ֥וֹת אֶת־כָּל־חַ֖י כַּֽאֲשֶׁ֥ר עָשִֽׂיתִי׃God said to Himself: "Never again will I doom the earth because of man, since the devisings of man's mind are evil from his youth; nor will I ever again destroy every living being, as I have done."
Leaving aside the question over "evil from his youth," about which much of rabbinic tradition disagrees, the essence is clear: God felt remorse, and learned from what might be called a mistake.
Just like God, we learn from our mistakes as well. We change, we grow, we mature. The rainbow (and its berakhah) therefore remind us not only of the covenant, but also our ability to transcend errors of the past and improve ourselves.
Rabbi Seth Adelson