The relationship serves to characterize both Goneril and Regan. Neither has the decency, respect, or honor to remain loyal to their own husbands. Also, the relationship highlights a theme of the work, the disorder of family. Goneril and Regan usurp their father's authority and they disrupt the bonds of marriage. Finally, this conflict serves literally in the plot as the cause of death for both Regan and Goneril. Out of jealousy over Edmund, Goneril poisons Regan, and later kills herself after confessing to murdering her sister.
The tangled web of affection, romance, manipulation, power, and betrayal among Goneril, Regan and Edmund has finally taken on a clear shape. The purpose for this was to show us a main theme of the story- the disorder and the madness of the family