After the Israelites rejected the desirable land, the fate of the desert generation was sealed with a severe and final consequence. God decreed their destruction, permanently barring them from entering the Promised Land [מלבי״ם].
To express the absolute certainty of this decree, God made a solemn oath. This act is portrayed through the vivid human imagery of raising a hand toward the heavens, just as people do when swearing [אבן עזרא]. The divine oath was directed specifically at the people and was a direct result of their actions [רד״ק, מצודת דוד], sealing the decree upon them personally [אלשיך].
God swore to punish all those who had complained against Him [רד״ק]. The tragic outcome was that the entire generation would die, and their bodies would fall in the very desert where they wandered [אלשיך, ביאור שטיינזלץ]. This specific punishment ensured that the people would never merit entering the land they had so deeply despised [מלבי״ם]. This echoes God's explicit declaration in the Torah, where He swore that the men who rebelled against His word would meet their end and die in the wilderness [מאירי].