וְהָיְתָ֥ה הַקֶּ֖שֶׁת בֶּֽעָנָ֑ן וּרְאִיתִ֗יהָ לִזְכֹּר֙ בְּרִ֣ית עוֹלָ֔ם בֵּ֣ין אֱלֹהִ֔ים וּבֵין֙ כָּל־נֶ֣פֶשׁ חַיָּ֔ה בְּכָל־בָּשָׂ֖ר אֲשֶׁ֥ר עַל־הָאָֽרֶץ׃
At ang bahaghari ay mapapasa ulap; at makikita ko ito, upang alalahanin ko ang tipang walang-hanggan sa pagitan ng Diyos at ng bawat nabubuhay na nilalang sa lahat ng laman na nasa ibabaw ng lupa.
Rashi
בין אלהים ובין כל נפש חיה BETWEEN GOD AND EVERY LIVING SOUL — Between Divine Justice and you; for otherwise it should have written “between Me and every living thing”. But this is its explanation: when Justice will come to accuse and condemn you I will look upon the sign and remember the covenant (see Genesis Rabbah 35:3).
Radak
והיתה הקשת בענן, it will be there as a sign, וראיתיהו לזכור, a figure of speech, as already commented upon by us elsewhere. Rabbi Avraham Ibn Ezra writes that actually, the rainbow is not a passing phenomenon but is in the clouds or sky at all times but at times is visible only to G’d.
Sforno
וראיתיה לזכור ברית עולם, I will take a close look at how the righteous of that time call the ordinary people to order, and whether their prayers are on behalf of their contemporaries. If they make their weight felt, I, in turn, will remember My covenant in their favour, and My wrath at them will be turned aside.