The theme of parent-child relations is so important to the meaning of King Lear that one could write a book about it. To name the heart of it, though, Lear shows that he misunderstands the way in which a daughter's love to her father should /must be expressed, and fundamentally misjudges Regan and Goneril, taking their flattery at face value. However, if he misjudges those two, his judgment of Cordelia is something close to a crime. He so underestimates her love that he blasts her in the opening act.
The rest of the play then dramatizes what happens when these relationships go bad, with Cordelia embodying what a daughter should be and do for her father.