The significance lies in the fact that Malcolm is now the heir to the throne, something that wasn't told to Macbeth, nor was he told when he would become king. So, Malcolm is now a new obstacle for Macbeth, which is significant, but it is also significant in that it reveals Macbeth's ruthless ambition, for he is not thwarted by it; instead, he asks the "Stars, to hide [their] fires" so that noone will know of his "black and deep desires." It appears that Macbeth has become more determined to go through with assasinating Duncan, despite Malcolm becoming the Prince of Cumberland. It appears that Macbeth is not thinking clearly revealing just how blind he has become by his "vaulting ambition."
Duncan's naming Malcolm Prince of Cumberland in Act 1:4 of Shakespeare's Macbeth is significant because it means if Macbeth is ever going to be king as the witches predict, it will take more than natural means for him to be so. It practically ensures that Macbeth will have to eliminate Duncan to snatch the thrown.
Macbeth realizes this immediately:
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,
The eye wink at the hand; yet let that be
Which the eye fears, when it is done, to see.
Macbeth knows that Malcolm being officially named Duncan's heir is an obstacle that he must get by or stumble on, and he knows this means killing Duncan. He metaphorically asks to be hidden as he does so, and to do what the eye will be afraid to see once it is done.
Of course, because Malcolm is by the time of the assassination the heir to the throne, Macbeth would have had to kill him, too. But Donaldbain and Malcolm are wise enough to flee after their father is killed (Act 2.3). Malcolm lives to raise an army and return to Scotland to claim is rightful thrown.