When Macbeth wants to back out of the plan to kill Duncan and take his throne, his wife resorts to insulting and emasculating him in order to compel him to resubmit to her will. She asks him,

Art thou afeard
To be the same in thine own act and valor
As thou art in desire? Wouldst thou have that
Which thou esteem'st the ornament of life
And live a coward in thine own esteem [...]? (1.7.43–47)

She accuses him of lacking the courage to do the things he needs to do to get what he wants. She suggests that he will have to think of himself as a coward for not taking this opportunity to snatch the crown if he chooses not to move forward. Lady Macbeth first implies that he is not really a man and then directly says so. She tells him,

When you durst do it, then you were a man;
And to be more than what you were, you would
Be so much more the man. (1.7.56-58)

In other words, she says to him, you were a real man when you were willing to do this deed, and if you would choose to do it now, then you would be more than a man. The implication, of course, is that if he chooses not to do it, then he is certainly not a man. He is "unmade," she says, by the fitness of the time and place; the couple has the opportunity to take the throne tonight, and now Macbeth is suddenly unwilling. Lady Macbeth is, obviously, a woman, and her husband is supposed to be more powerful, more strong and courageous and ruthless than she is. When she belittles and emasculates him in this way, she seems to assume the dominant position in their marriage, making him feel powerless. She hits him where it hurts, in his pride, again and again, and the quotation you cite is just another example of this. She talks about how she would kill her own baby if she had promised Macbeth she would rather than break that promise to him, implying that she is more of a man than he is.

At the beginning of Act I, scene viii, Macbeth has persuaded himself not to murder Duncan after all. Lady Macbeth manages to change his mind, forcing him into a 180 degree turn with her powerful rhetoric. These are her most terrifying and unforgettable lines:

I have given suck, and know
How tender 'tis to love the babe that milks me:
I would, while it was smiling in my face,
Have pluck'd my nipple from his boneless gums,
And dash'd the brains out, had I so sworn as you
Have done to this.

The literal meaning here is simple. Lady Macbeth has had at least one child (leaving Shakespeare scholars to speculate endlessly on what happened to him, her or them). She knows how much a mother loves her children. However, she would rather have wrenched the baby from her breast and smashed his or her skull against the nearest wall than break a solemn oath.

This is a shocking image and is clearly intended to be so. It is easy to act with revulsion, as though Lady Macbeth were actually confessing to infanticide. What she is actually doing, however, is using the most appalling idea she can imagine to emphasize what a disgraceful thing it is to break one's word. If she were not goading Macbeth on to commit a terrible crime, she might have a point. In any case, it is clear from this passage that she does not take infanticide likely, but regards it as a terrible crime. It is unfortunate for Macbeth, and for her, that she does not feel the same about regicide.

Macbeth is having second thoughts about killing Duncan, although he had already discussed and planned doing so with his wife. Now that Duncan is under his roof, Macbeth begins to remember what a good king Duncan is, that he, Macbeth, owes him protection for being in his castle, and that once he kills Duncan, he will have headed down a path that will only become more and more bloody. He hesitates because he realizes there will be no turning back once the deed is done. This is a very serious business indeed.

Lady Macbeth, however, has no such qualms. She wants the crown, and she wants it now. She wants Macbeth to be king. As she sees him waver, she realizes it is now or never. She must galvanize him into action or it will never happen. Macbeth will continue to talk himself out of acting.

Lady Macbeth therefore pulls out all the stops. She says that if she had promised to do something even so unnatural as to kill her infant, she would honor that promise. She says in this quote that she would pull the baby off her breast as it was suckling and dash its brains out. She makes clear that is the way a strong person behaves. She knows which buttons to push to persuade her husband to act. Anything less than Macbeth honoring his promise to kill Duncan would be unmanly and cowardly. After all, if she, a woman, could kill her own helpless baby, in theory, how could he, a soldier, have qualms about killing a grown man?

When Macbeth falters in his plan to murder the King Duncan, Lady Macbeth uses this line to force Macbeth into action. She is telling him that if she had made a promise to him, even if it was to kill her newborn baby by bashing his brains out, she would not faulter in her promise. In a way she is telling Macbeth that she is more committed to him than he is to her. She is also telling him that he is weak and less of a man if he is unable to follow through with their plan, when she would be willing to kill her own blood. She is manipulative in her words and this is what forces Macbeth into action.

Have the MacBeth's had children in the past? This quote indicates that Lady MacBeth has had a child in the past, perhaps the fact that their child has died has led the MacBeths to rely on each other a lot, feel depressed or even for Lady MacBeth to become unbalanced. Perhaps she looks to compensate for the loss of her child by ambition for her husband.

In the context of this speech she is showing MacBeth that in stepping back from what she considers he has to do - murder Duncan and become king - he is a coward and is letting her down badly. The image she gives here of the killing of a child is an appalling one, the idea of dashing out the brains of a child deliberately revolts us and turns us against Lady MacBeth. It also shows the sheer force of her character that leads to MacBeth following what she says.