The expression occurs four times in the Bible:

1) Referring to Israel:  "In a desert land he found him, in a barren and howling waste.  He shielded him and cared for hm; he guarded him as the apple of his eye" (Deuteronomy 32: 10);

2) Referring to David:  "Keep me as the apple of your eye; hide me in the shadow of your wings" (Psalm 17: 8);

3) Referring to Solomon's teaching:  "Keep my commands and you will live; guard my teachings as the apple of your eye" (Proverbs 7: 2); and 

4) Referring again to Israel:  "For this is what the Lord Almighty says:  'After he has honored me and has sent me against the nations that have purchased you--for whoeer touches you touches the apple of his eye" (Zechariah 2: 8).

The expression is an ancient one, and the most prominent explanation of its origin is this:  In biblical times the black pupil of one's eye was thought to be a small globe, not a hole.  An apple is one of the most common spherical items of everyday life; thus, the pupil came to be called the "apple" of the eye.  Since sight is widely regarded as our most precious sense, and the "apple of the eye," is the entry point of light into the body, something (or more often someone) particularly precious to you is referred to metaphorically as the "apple of your eye."