I actually think that the word is quite a fascinating one in the play. Ms-mcgregor gives you a good gloss of it above, and its meaning in the prophecies scene. Yet it also comes up lots of other times, and when it does, it seems to me often to imply its opposite: that is, "doubling" something in Macbeth seems to mean that it isn't there at all.
He's here in double trust;
First, as I am his kinsman and his subject,
Strong both against the deed; then, as his host,
Who should against his murderer shut the door,
Not bear the knife myself. (1.7)
Duncan trusts "double" - he should actually not trust at all. And here's Lady Macbeth talking about how much she wants him to come to the house (she's going to murder him!):
All our service
In every point twice done and then done double
Were poor and single business to contend
Against those honours deep and broad wherewith
Your majesty loads our house... (1.6)
Later, Macbeth decides not to kill Macduff because of the prophecy that he himself can't be killed:
Then live, Macduff: what need I fear of thee?
But yet I'll make assurance double sure,
And take a bond of fate. (4.1)
This "assurance", of course, doesn't actually involve killing Macduff. It doesn't assure anything at all. And finally, Macbeth realises that the "doubleness" of the witches' advice makes it entirely useless:
And be these juggling fiends no more believed,
That palter with us in a double sense. (5.8)
Strange, isn't it?
In Act IV, scene 1, the witches are casting some kind of spell. After the ingredients for the incantation are put in a pot, all three say:
"Double, double, toil and trouble;
Fire burn and cauldron bubble."( IV,i,34-35)
The significance of the word double is just was the would "double" means, to increase by two times. They want twice the trouble and toil
( hard work) to come on their victim as would usually occur.However, this is also a a reference to the double meanings of the predictions the witches are about to give Macbeth about his future.
After they use the word "double, double" they chant three times to make sure all three predictions they will make will be powerful.
Macbeth then appears and asks the witches about his future. The witches are call upon three spirits or apparitions to tell him his future. Although the things the apparitions tell Macbeth are true, they are full of double meanings that Macbeth does not understand. Especially meaningful are two messages. One tells him he will not be killed by an man borne of a woman. This leads Macbeth to think no man can kill him. The other prediction is that Macbeth will not be defeated until, “Great Birnam Wood to high Dunsinane Hill shall come against him.” Macbeth believes that having a forest move is impossible and so once again he feels falsely secure. However, both prophecies have double meaning that the audience can consider, but Macbeth does not and he is lead to his downfall.