This is an excellent question as this play presents us with a man that is essentially tortured by visions of the future that deliberately mislead him and give him false security. The witches' predictions come to plague Macbeth as a character. You might find it worthwhile to analyse one prophecy in particular from Act IV scene 1, when Macbeth goes out to find the witches and demands the "truth", whatever the destruction that may befall the world.
However, it is important to note how the truth that is revealed here, as in other places in the play, plays with his insecurities and leads him on into ever greater acts of darkness and evil. When the third apparition comes, described as "Third Apparition, a child crowned, with a tree in his hand" in the stage directions, Macbeth responds:
What is this,
That rises like the issue of a king;
And wears upon his baby brown the round
And top of sovereignty?
It is important to note that the crown not only completes and rounds, as with the perfection of a circle, the claim to sovereignty, but it is figuratively the summit of his ambitious hopes. Macbeth can thus interpret this sign in terms of his own success in keeping the crown and producing an heir, though the significance of the tree is explained by the third apparition itself:
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.
Therefore the tree represents the danger in the future prophecy of Dunsinane wood moving against Macbeth and attacking him - the prophecy that becomes terrifyingly true in Act V. Note how this prophecy gives Macbeth false hope and confidence - it is as if the witches are deliberately playing with Macbeth's mind, giving him faith and hope, yet knowing that he will be deposed and the future that Macbeth is clinging on to will come to naught. Thus the confidence and faith Macbeth has in the prophecies is a major part of his downfall.