לְמַ֣עַן הָקִֽים־אֹתְךָ֩ הַיּ֨וֹם ׀ ל֜וֹ לְעָ֗ם וְה֤וּא יִֽהְיֶה־לְּךָ֙ לֵֽאלֹהִ֔ים כַּאֲשֶׁ֖ר דִּבֶּר־לָ֑ךְ וְכַאֲשֶׁ֤ר נִשְׁבַּע֙ לַאֲבֹתֶ֔יךָ לְאַבְרָהָ֥ם לְיִצְחָ֖ק וּֽלְיַעֲקֹֽב׃

God is enacting this covenant with you in order to establish you today for Him as a people, and He will be your God. There are two parties to the covenant, which entails an exclusive, mutual relationship between the children of Israel and God, as He spoke to you, and as He took an oath to your forefathers, to Abraham, to Isaac, and to Jacob. God’s oath to the patriarchs continues with His oath to their descendants.

וְלֹ֥א אִתְּכֶ֖ם לְבַדְּכֶ֑ם אָנֹכִ֗י כֹּרֵת֙ אֶת־הַבְּרִ֣ית הַזֹּ֔את וְאֶת־הָאָלָ֖ה הַזֹּֽאת׃

But not with you by yourselves do I make this covenant and this oath;

כִּי֩ אֶת־אֲשֶׁ֨ר יֶשְׁנ֜וֹ פֹּ֗ה עִמָּ֙נוּ֙ עֹמֵ֣ד הַיּ֔וֹם לִפְנֵ֖י יְהוָ֣ה אֱלֹהֵ֑ינוּ וְאֵ֨ת אֲשֶׁ֥ר אֵינֶ֛נּוּ פֹּ֖ה עִמָּ֥נוּ הַיּֽוֹם׃

rather, I am establishing the covenant and the oath with him who is here with us standing today before the Lord our God, the entire assembly who are present, and also with him who is not here with us today. This is referring either to people who were unable to participate in the assembly, or to future generations and converts who will later join the people.