Macbeth is most concerned with two things when he visits the Witches in Act IV, scene i: Will he be murdered as he murdered Duncan? And, since he and Lady Macbeth have no children, who will follow him as king? The two children apparitions are symbolic representations of those who might bear the power to take his life.
The bloody child is called the Second Apparition, and it says:
Be bloody, bold, and resolute; laugh to scorn
The power of man, for none of woman born
Shall harm Macbeth.
The image of a bloody child, besides being just the sort of gore that Shakespeare's audience enjoyed, suggests a child who is born in blood, naturally birthed from his mother's womb.
The crowned child, or Third Apparition, carries a tree in his hand. He says:
Be lion-mettled, proud; and take no care
Who chafes, who frets, or where conspirers are.
Macbeth shall never vanquish'd be until
Great Birnam wood to high Dunsinane hill
Shall come against him.
This apparition is crowned to suggest that the kingship is at stake. It carries a tree to suggest the wood that it speaks of, but also to foreshadow how the seemingly impossible task of the wood "coming" from one place to another. It will be carried as camouflage for the soldiers who make a sneak attack upon Macbeth.
Both apparitions are technically correct in their assessments. Macbeth is not killed by a man of woman born, but a man born by Cesarean section, and the wood moves from one place to another, not because it grows legs and walks, but because its sticks and branches are carried by the soldiers coming to defeat Macbeth.