Many times I have heard parents say their children are the "Apple of their eye," and here we see the psalmist asking God to keep him as such. God made us in his image, and this verse is a reminder that we are his children and we want him to protect us young birds (children) keep hidden under their parents wings. And he will. He is the shepherd who will leave his 99 sheep just to find the one, because we are all special and all loved.
I pray daily for God's protection for myself, my family, and the world.