Duncan names his son Malcolm the Prince of Cumberland. What do the following lines (48-51) show us about Macbeth's feelings on this matter?
"The Prince of Cumberland! That is a step / On which i must fall down or else o'erleap, / For in my way it lies. Stars, hide your fires; / Let not light see my black and deep desires." These are the lines I'm referring to in the question.
Macbeth's words reveal that he is more bent on becoming the king of Scotland by murdering Duncan than before. If you recall in scene 3 of Act I after Macbeth has the "horrid image" that "doth unfix" his hair which is the frightening thought of murdering Duncan, he states that "If chance will have me king, why, chance may crown me / Without my stir." In other words, if fate wants him to become king, perhaps fate will just make it happen without Macbeth having to do anything, like murder the king.
But after Maceth hears that Malcolm is named the Prince of Cumberland, he is more determined than ever to go through with the "horrid image" he had in scene 3, so much that he calls upon the stars to hide their "fires," or light, so that noone will know his "black" or evil desires, those being to become king by murdering him.
Macbeth is back on the path of manipulating fate.
In the play 'Macbeth' by William Shakespeare, we see Macbeth begin to hide his feelings from his friend and battle colleague for the first time. Just after the witches tell him he will be king, he disguises his interest in this prophecy from his companion. Now, he is going one step further and this is part of the slippery slope towards deceit, lies and murder. It is said that once a person begins down this road, or begins to lie, then they may feel that they have to lie more and more, with bigger and lies and atrocities to cover up the first misdeed. These words show Macbeth's two-faced-ness, and we are let in on the act. He shows one face to friends and visitors, while underneath a boiling sea of self-interst,ambition and madness lies. The interesting thing is that 'let not light see my black and deep desires' shows that Macbeth himself is aware of his own 'fall' - and that would be worrying even for a criminal psychologist today.
What Macbeth's words here show is that he now sees Malcolm as an obstacle -- a step that he must get over.
This is because the witches have just told him he will be the Thane of Cawdor and the king. Right after that, he hears that he has been named the Thane of Cawdor. Once he hears that, he starts thinking that the witches are right and that he will become the king.
When he hears Duncan has named Malcolm Prince of Cumberland, he figures that he'll have to get rid of Malcolm and the king if he wants to be king himself.
The part about the stars just means that he has to hide his ambition (to become king) from everyone.
Macbeth only see Malcolm as a stumbling block to his ascension to the throne. In other words, Malcolm is just something Macbeth has to overcome...step over. If he is tripped up by Malcolm, he will not become King. Macbeth must keep his true intentions secret. Under the cloak of not will he attempt all his schemes, and make Malcolm appear to be the fall guy.