The apple of the eye was the term used to refer to the pupil of the eye as it was thought to be solid. It is very old as an idiom, and is used to say that something is particularly precious to you. Why this should be is lost in the mists of time.
I love all my daughters, but the youngest is certainly the apple of my eye. - the person who someone loves most and is very proud of.
pun: She was the apple of my eye until she started keeping it peeled.
The new Apple iMac is the darling of the computer industry.
Facebook has become the latest darling of the Web 2.0 internet world.
Leonardo DiCaprio was the darling actor of the movie industry after the movie "Titanic" become an epic.