The relationships between Lear and his three daughters are the most significant relationships in the play.
Though the character of the fool presents an important source of commentary and is highly relevant to the development of the themes of the play, it is the father-daughter relationships that A) drive the plot of the play and B) symbolize and structure the central themes of the play.
The importance of Lear's relationships with his daughters in terms of the plot is straight-forward. Lear divides his kingdom between two of his daughters and disowns the third daughter. This action leads directly to Lear's predicament; his angst; his crisis.
Thematically, these relationships demonstrate the nature of Lear's unnatural actions.
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.
Lear casts off the love of one daughter because she refuses to act unnaturally in proving her affections for her father and splitting her loyalty between husband and father.
Lear has chosen an awkward and arguably inappropriate moment to ask his only unwed daughter to declare him the sole object of her love.
Despite acting in accordance with a real wisdom (which Lear does not recognize), Cordelia is cast out. This act proves Lear's hubris as he insists that the natural order of family be overthrown in favor of his desire. Cordelia remains loyal through it all. This is a natural loyalty that is given a chance to be fully articulated by Lear's choice to disown Cordelia.
Lear's other daughters follow his own example of corruption. The power of his position as king has perverted his sense of his role in nature. The same type of power corrupts Goneril:
Goneril's increasingly cruel treatment of Lear is proof of the adage that "power corrupts."
Where it is natural for daughters to love their fathers, and fathers to love their daughters, the politics of power serves to corrupt this natural set of dynamics. This is an important aspect of the play and it is examined through the example of Lear's relationships to Regan and Goneril.