There are plenty of quotes that have significance, but to give you one that seems to be to stand out as being particularly important in terms of the overall play, I would want to choose Cordelia's response to her father. Let us just remind ourselves of the context. Lear wants each of his daughters to tell him just how much they love him, and he will award his kingdom and power according to their responses. We have seen Regan and Goneril engage in insincere lies and flattery designed to try and get as much from their father as possible. In sharp contrast to her sisters, Cordelia, Lear's most-loved daughter, says the following in Act I scene 1:
Unhappy that I am, I cannot heave
My heart into my mouth. I love your majesty
According to my bond; no more nor less.
Although lacking in flattery, Cordelia actually expresses a deeper and sincerer and more valuable love than the lies of her sisters, as she loves her father "according to my bond," which means she accepts without hesitation her responsibility and duty to love him, both in his role of father and king. It is clear that Cordelia has a genuine love for her father, but she refuses to "heave / My heart into my mouth" and exaggerate her feelings with falsehoods for her own personal gain, as her sisters have just done. It is Lear's response to these words and his ironic inability to perceive, understand and appreciate the genuine love that they contain that initiates the tragedy of this play. This quote is therefore important because their lack of flattery demonstrate the depth of her love whilst emphasising her father's foolishness and lack of ability to perceive the truth about his daughters and how they regard him respectively.