According to the author of 1 Samuel, God chose David, the youngest son, who was taking care of sheep, to be special. Samuel wanted to meet him because he was important for God's plan.
1 Samuel 16:11: And Samuel said unto Jesse, Are here all [thy] children? And he said, There remaineth yet the youngest, and, behold, he keepeth the sheep. And Samuel said unto Jesse, Send and fetch him: for we will not sit down till he come hither. [down: Heb. round]
This passage lists David as the seventh son, while 1 Samuel 16:11 suggests he is the eighth.
1 Chronicles 2:13-15: And Jesse begat his firstborn Eliab, and Abinadab the second, and Shimma the third, [Shimma: or, Shammah]