Lear's relationships with his daughters are important to the overall meaning of the play. In his relationships with his three daughters, the nature of Lear's roles are developed: as king, as father, and as a person who "gives up" these positions.
Lear has a "natural" relationship with only one of his daughters (through no virtue of his own, but due to Cordelia's great honesty, intergity and loyalty). With Cordelia, in the end, Lear realizes that he has no power to reverse or alter the "natural order" that defines the relationship between father and daughter. Though he attempts to disown and disavow Cordelia, he comes in the end to recognize that she is his "true daughter".
This state is in direct contrast with Lear's relations with his two other daughters. Cordelia's love for Lear is unconditional, but that of Regan and Goneril proves to be definitively conditional.
The position of authority that Lear occupies at the opening of the play is respected by Goneril and Regan. As long as Lear possesses wealth and power to be distributed, these daughters fawned falsely over him. When he chooses to remove himself from power, giving away his wealth and power, Goneril and Regan lose both respect and affection for him.
...when [Goneril] sees that she can manipulate her weakened father, the sense of her own power seems to go to her head.
Ultimately, these relationships function as engines of action moving the plot forward and as evidence of the effects of challenging or denying the "natural order" of the world. Lear and his daughters all suffer in direct proportion to the degree to which their relationships have been corrupted or perverted.
From a traditional perspective, Lear's downfall is the result of a tragic flaw in his character: his majestic sense of himself is not bounded by the norms of the natural order.