Why are Macbeth's visions related to children?
After Macbeth first visits the witches and receives prophecies of prosperity that come true, he sees fit to visit them again when his life takes a downward turn. The second visit results in prophecy from the "masters" through various visions, which all include images of children.
The first image is that of a armed head, or a head in armor who announces "Beware Macduff. Beware the Thane of Fife." (IV,iv). We are not sure if the wearer is a child, but it stands to reason that it is either the head of Duncan's son Malcolm, who ultimately avenges his father's murder and takes the throne or the head of Fleance, the child who survives Banquo's murder. Banquo was prophesied to be the father of kings.
The second image is that of a bloody child who announces:
Be bloody, bold and resolute. Laugh to scorn
The power of man, for none of woman born
Shall harm Macbeth. (IV,iv)
This vision most likely corresponds to MacDuff, who is later revealed as "...From his mother's womb untimely ripp;d"- a reference to a crude C-section procedure performed on an already dead mother.
The third and final image is that of a child with a tree branch in his hand. He assures Macbeth that he will "never be vanquished" (IV,iv) until the woods of Birnman physically march up Dunsinane hill to his castle. This seems and impossibility to Macbeth, making him more assured.
Finally, Macbeth wishes to know if there is any chance Fleance, Banquo's son, will ever rule. His answer is a series of mirrored images of the child Fleance reflected over and over and ending with Banquo. Again, this hints to the idea that Banquo's children will ultimately rule the land.