Explain this quote from Macbeth: "Glamis thou art, and Cawdor; and shalt be what thou art promised" to show Lady Macbeth's ambition?
Lady Macbeth speaks these lines in Act I after reading a message from her husband, Macbeth. Earlier in Act I, Macbeth and his friend and fellow military leader, Banquo, come across three witches out on the heath after a battle. The witches give both men prophecies; Macbeth is told he will become Thane of Cawdor and King of Scotland. Minutes later, some men sent by the current King, Duncan, inform Macbeth he has been named Thane of Cawdor after the former thane was found to be a traitor (he will be executed and his position reassigned by the monarch). Following this encounter, Macbeth sends a message ahead to his wife back at their castle at Inverness, and in this note, he reveals the prophecies to her. What we see in this quote is Lady Macbeth's immediate reaction to this message.
Lady Macbeth first repeats information we already know: that Macbeth is now both Thane of Glamis (his old title) and Thane of Cawdor (his new title). Lady Macbeth then states that Macbeth "shalt be/ What thou art promised" (I.v.16-17). This means that Lady Macbeth takes the prophecy at its word and implies that she is willing to do whatever it takes to ensure that it does indeed come true. Lady Macbeth's choice of words here - "shalt be" -- reflects her belief that either his position as king is guaranteed by fate/destiny or that it will be because he, she, or both he and she will make it so. This hearkens back to a comment Macbeth makes in Act I, scene iii, after hearing the prophecies: "the greatest is behind" (I.iii.123). That statement indicates that Macbeth believes the prediction that he will be "king hereafter" is actually true.
Lady Macbeth's comment in these lines indicates that she has ambition in the sense that she wants her husband to be king and she wants to be queen. It is somewhat unclear what her personal ambitions are, but it is clear that she wants her husband to be in power, and, of course, she will benefit from that power, as well. Immediately after these lines, Lady Macbeth continues her famous soliloquy, in which she reveals her fear that Macbeth is too kind and too meek to actually go through with murdering the king in order to quickly ensure his own rise to the throne. She also reveals more about her own ambition in the part of the soliloquy where she laments that she is a woman and wishes to rid herself of her feminine qualities so she could simply kill Duncan herself. This indicates that her ambition for power is strong but she also is aware of the limitations placed on her by her gender. The only way her own ambition can be satisfied is through Macbeth, so she must support his rise to power to have access to her own.
The quotation "glamis thou art, and Cawdor; and shalt be what thou art promised" shows Lady Macbeth's concern for her husband's ambition rather than her own ambition. I would prefer to say that Lady Macbeth's resolve to stand by her husband's ambition for kingship is an act of volition born of the wife's loyalty towards the husband. Although Lady Macbeth would have been the queen in case Macbeth could ascend the throne, Lady Macbeth seemed to have been driven more by her urge to work for her husband's ambition than by any selfish ambition of her own. She mainly suffers for this misguided act of conjugal loyalty. She invokes the powers of darkness to enable her in favor of working out the murderous design.