According to Saul, the decision to spare the animals was so that they could be given in sacrifice to the Lord (1 Samuel 15:15, 1 Samuel 15:21). Presumably they would not be sacrificed as burnt offerings (Leviticus 1:1–17) but rather as thanksgiving/fellowship offerings (Leviticus 6:11–21) since this would enable the men to also enjoy some of the meat.1 With this arrangement, the animals were given to the Lord and the men got to enjoy a hearty meal.
9 But Saul and the people spared Agag and the best of the sheep and of the oxen and of the fattened calves and the lambs, and all that was good, and would not utterly destroy them. All that was despised and worthless they devoted to destruction.