The tactic that Malcolm uses is to have everyone in his army cut a branch from a tree in Birnam Wood and use the branch for camouflage. The hope is that people seeing the army from a distance will mistake it for a forest (seems like an odd ploy since people ought to know where the forest should and should not be).
The significance for the play is that it fulfills the witches' prophecy. They said that Macbeth could not be defeated until Great Birnam Wood came to Dunsinane. When Malcolm has his army cut the branches, Birnam Wood is coming to Dunsinane and Macbeth will soon be defeated.
Malcolm and King Edward's soldiers have encamped close to Birnam Wood not far from Macbeth's castle. Malcolm gives the following instruction to the troops:
Let every soldier hew him down a bough
And bear't before him: thereby shall we shadow
The numbers of our host and make discovery
Err in report of us.
He is, in effect, ordering every soldier to cut down a tree branch and hold it before him. He states that, in doing this, they will disguise their numbers and, therefore increase the probability that the true number of soldiers will be reported incorrectly. This is a clever camouflage tactic because Macbeth has no idea how many soldiers King Edward of England has provided Malcolm with in his effort to overthrow him and retake Scotland.
If one were to view, from a distance, the soldiers thus disguised marching towards Macbeth's castle at Dunsinane, it would seem as if the forest itself was on the move. When Macbeth is informed that the forest is moving, he reacts angrily:
As I did stand my watch upon the hill,
I look'd toward Birnam, and anon, methought,
The wood began to move.
If thou speak'st false,
Upon the next tree shalt thou hang alive,
Till famine cling thee: if thy speech be sooth,
I care not if thou dost for me as much.
I pull in resolution, and begin
To doubt the equivocation of the fiend
That lies like truth: 'Fear not, till Birnam wood
Do come to Dunsinane:' and now a wood
Comes toward Dunsinane.
Macbeth expresses his despair because he now realizes that the witches' prediction that
Macbeth shall never vanquish'd be until
Great Birnam wood to high Dunsinane hill
Shall come against him
was, in fact, an equivocal declaration that he believed in a literal sense. He believed the witches meant that the forest would literally uproot itself and march towards his castle—an impossibility. At the time he saw these as "sweet bodements." He now expresses doubt about the veracity of the witches' prognostications and finally realizes that they were deliberate lies meant to deceive him.