What does it mean when the question is why does Lady Macbeth apply the spur in Macbeth? The quotation is: "That tears shall drown the wind. I...

In the above quotation, Lady Macbeth is considering her
role in trying to persuade Macbeth to follow his ambition to become king by murdering
Duncan.  The line "I have no spur to prick the sides of my intent" means that Lady
Macbeth knows that she herself has no real reason to want Duncan dead--she only wants
him dead so that her "vaulting ambition" may push her husband into action.  Later, Lady
Macbeth convinces her husband that he deserves to be king, and thereby "applies the
spur" to induce action.  Earlier, when Lady Macbeth receives the letter from Macbeth
detailing the witches' prediction, Lady Macbeth knows that her husband will likely not
act on his inner desires because she thinks he is too good a person to go after what he
wants.  So, she knows that her ambition will have to overtake his in order to occupy the
throne.