Writing: How do we create deep, vibrant characters within a story?

A reader question:
My question is, how do you balance the need to cut out the large amounts
of extraneous material about a character's background versus the desire
to provide the reader with deep, vibrant characters with whom they can
relate? I understand now more about how to place hints via dialogue and
action, but I am concerned about leaving my characters too shallow.


How do we create deep, vibrant characters within a story?

A long description of a character, his/her antecedents, personality tr...