This is very important; it shows that Macbeth trusts his wife with everything. Another indication of their relationship in the phrase "my dearest partner in greatness". This suggests that Macbeth loves his wife dearly, but not only that, but considers her his equal. At the time this play was based, or even written, women were very much considered inferior. She also perhaps, reveals, a weaker side to her personality when she prays to the dark powers to fill her heart with cruelty, and rid her of feminine kindness. If she were truly evil, then she would not need this extra infusion of darkness. This is an interesting point because it reveals a whole new side to her, which while it isn't a good side; it is a more human side. It proves that she is not a witch, perhaps, as some people think.
When Macbeth enters, they greet each other warmly, and Lady Macbeth reveals her intentions to murder King Duncan, and persuades Macbeth to go along with the idea, and warns him to greet the King warmly and not give any indication of their plans. It is important how Lady Macbeth persuades Macbeth, she uses veiled talk, and double meanings to attempt to sweeten the idea, she never mentions the word murder, rather, and just notes that Duncan will not see the sun rise tomorrow. It is a form of seduction almost, she hides the foul ideas behind pretty words, making it seem as if it is all right. When Macbeth tries to interject, she simply speaks over him, soothing his now troubled mind with a promise that she will handle everything else, as long as he keeps an innocent face.
The next scene is Lady Macbeth welcoming Duncan and the others into her and Macbeth's castle, and true to her own advice, she is warm hearted and kind. All the while knowing that she intends to kill him. She is the perfect hostess, and makes several remarks on how much she thanks Duncan for rewarding her house with his presence. This is extremely two-faced of her; she greets him with smiles, while practically holding a dagger.