Adam Clarke on 1 Samuel 15:2

I remember that which Amalek did - The Amalekites were a people of Arabia Petraea, who had occupied a tract of country on the frontiers of Egypt and Palestine. They had acted with great cruelty towards the Israelites on their coming out of Egypt. (See Exo 17:8 (note), and the notes there). They came upon them when they were faint and weary, and smote the hindermost of the people - those who were too weak to keep up with the rest. (See Deu 25:18). And God then purposed that Amalek, as a nation, should be blotted out from under heaven; which purpose was now fulfilled by Saul upwards of four hundred years afterwards!