What is the meaning of the phrase "the apple of his eye"?

The phrase is an idiom that means that someone really cares about someone else. 

An idiom is an expression or figure of speech that is so commonly used that everyone knows what it means, even if it seems to make no sense on its own.  Other examples are “it’s raining cats and dogs” (for heavy rain) or “to beat around the bush” (to take a long time to tell someone something).  Sometimes expressions have been around so long that their original meaning is lost, but they are still commonly used so everyone knows what they mean. 

When you say someone is the “apple of his eye” it means that he really likes someone, cares about someone, or is proud of someone.  Usually this refers to a parent and child.  For example, a father might have a son who is the apple of his eye.  This means that the father is very proud of his son and loves his son very much. 

Versions of this phrase appear in the Bible, which is probably one of the reasons it is so popular.  It has also appeared in Shakespeare and other literature throughout the years and is a part of popular culture.  That is what makes it an idiom.