Meaning:

Be loved very much by someone.

If someone is the apple of your eye, you think he/she is very important to you, and you love him/her very much.
This idiom is used especially when someone is loved by an older member of his/her family.

Example:

Erika is Mark's only granddaughter, and she's the apple of his eye.

Sarah's only son was the apple of her eye.

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