Lady Macbeth says this line immediately after reading a letter she has just received from her husband. In that letter, Macbeth informs his wife that the witches have prophesied that he will be King. He is telling Lady Macbeth the news so that she might share in the joy that the prophesy has brought him, saying,
"This have I thought good to deliver thee my dearest partner of greatness, that thou mightst not lose the dues of rejoicing by being ignorant of what greatness is promised thee...Lay it to thy heart..." (I,v,10-13).
Lady Macbeth is indeed overjoyed, and in her excitement she reveals herself to be an extremely ambitious and unscrupulous woman. Her first inclination is to take things into her own hands, doing whatever it might take to make the prophesy come true, and come true as quickly as possible. To this end, she schemes to do away with Duncan, the current King, but she is afraid that Macbeth, although ambitious, is not as ruthless as she is. She is afraid that he is too kind by nature to do what needs to be done so that he can be King right away, and she voices her concern, saying,
"Yet do I fear thy nature, it is too full o' the milk of human kindness to catch the nearest way. Thou wouldst be great, art not without ambition, but without the illness should attend it" (I,v,16-20).
Lady Macbeth knows her husband is ambitious, but she is afraid he doesn't have the "illness", or the unscrupulous disregard for goodness, to act heinously and kill Duncan to gain the crown for himself.
The quoted lines occur in Lady Macbeth's first speech, a soliloquy, in act1 sc.5. On receiving her husband's letter in which Macbeth confides to Lady Macbeth how the witches predicted about his future, Lady Macbeth is all set to play the role of a loyal wife standing by her husband's desires as endorsed by the supernatural agency. Macbeth would be the thane of Cawdor, and also the king of Scotland, but for the lack of illness in his character without which no such high ambition is materialised:
Glamis thou art, and Cawdor, and shalt be
What thou art promis'd : yet do I fear thy nature;
It is too full o' the milk of human kindness
To catch the nearest way...
This is Lady Macbeth's reading of her husband's natural self. She believes that Macbeth is all too saturated with sympathy or kindness which is, nevertheless, a human virtue. She uses the metaphor of 'milk', it being a natural health drink for man. She suspects that because of too much of human sympathy Macbeth would not be able to 'catch the nearest way' which is Lady Macbeth's euphemism for the murder of Duncan--a shortcut to the throne. Therefore she must 'chastise' him with 'the valour' of her 'tongue'.