Have you ever been known as the "apple of someone's eye"? The "apple of the eye" refers to the center of the eye, so basically it is saying you are the focus of their attention.
In Psalm 17, David writes, "Keep me as the apple of your eye." Note that David says KEEP me as the apple of your eye. Since he writes "keep" we can see that David is not begging God to put him at the center of His attention. This is more David being thankful and asking for a continuation. David knows he is in the center of God's attention, and asks to remain there as he is still struggling with enemies. Which is why David will also ask God to "hide me in the shadow of your wings."
A mother bird will gather her chicks under her literal wings to protect them from weather or enemies. It is her way of hiding them from all that can bring them harm. God does the same thing for us under His wings. He holds us close and protects us from the "wicked" and "mortal enemies".
As we get into the New Testament we find that these mortal enemies are sin and death and the spiritual dark forces of evil. Isn't it great to know that we are such the "apple of His eye" that He sent His one and only Son? God so loved us and longed to hide us under his wing that He made the way for our sins to be forgiven that we would never have to be separated from Him but instead could have everlasting life. (John 3:16)
Today I can face the world knowing that God is watching over me, but He is also watching over you and everyone else! That is truly the most amazing part of this. God keeps us ALL as the apple of His eye. What a comfort that is, and what a great reminder of the "wonders of [His] great love"!