What does Lady Macbeth give up in order to be strong enough to convince Macbeth to kill Duncan?

She relinquishes her femininity through her "unsex me" speech. In Act 1, Scene 5, Lines 30-44, she pleads:

"Come you spirits

That tend on mortal thoughts, unsex me here,

And fill me from the crown to the toe top-full

Of direst cruelty. Make thick my blood.

Stop up the access and passage to remorse,

That no compunctious visitings of nature

Shake my fell purpose, nor keep peace between

The effect and it! Come to my woman's breasts,

And take my milk for gall, you murd'ring ministers,

Wherever in your sightless substances

You wait on nature's mischief. Come, thick night,

And pall thee in the dunnest smoke of hell,

That my keen knife see not the wound it makes,

Nor heaven peep through the blanket of the dark

To cry, 'Hold, hold!"

Lady Macbeth believes that it is not in a woman's nature to plot and help carry out the murder of someone else, especially to gain power.  Shakespeare's audience most likely would have had the same view of women.  So, when Lady Macbeth asks to be unsexed and requests that no "visitings of nature" convince her not to go through with Duncan's murder, she is asking that her womanhood (her nature) not take over her emotions and prevent her from carrying out what she considers a masculine act.  She is even afraid that once she carries out the deed that the reality of the murder will be too much for her to handle.  The men of her day are used to seeing gruesome battle wounds, so at the end of the speech she again requests to be more masculine in her reaction.

Shakespeare's portrayal of a woman in this sense is not unusual for him, but Lady Macbeth's speech is his most overt portrayal of his view of the differences between male and female natures.  He often portrays women as manipulative and cunning or more insightful than men (i.e., Portia from Merchant, Calpurnia from Julius Caesar), but the women often are not physically involved in what they are trying to get others to do.  Lady Macbeth believes that she is so close to this act that she must be able to respond to it as a man would.