Why does Macbeth decide to kill Lady Macduff and her kids?

Macbeth believes that Macduff is suspicious of him and he is trying to stop him from intervening. 

Macduff is a noble who is at Macbeth’s castle on the night he kills Duncan.  Macbeth is worried about the men who were there, including Banquo and Macduff.  He is concerned that they will be suspicious that Duncan’s murder was actually committed by the Macbeths.  When Banquo speaks up, Macduff agrees. 

Fears and scruples shake us:
In the great hand of God I stand; and thence
Against the undivulged pretence I fight
Of treasonous malice.

MACDUFF

And so do I.

ALL

So all.

MACBETH

Let's briefly put on manly readiness,
And meet i' the hall together. (Act 2, Scene 3) 

Macbeth therefore sends murderers after Banquo, his son Fleance, and the Macduff family.  Macduff happens to not be there. He is with Malcolm, the king’s son, who fled to England to gather an army to oppose Macbeth.  Therefore, the murderers kill Macduff’s wife and children.

Macbeth has no conscience.  He thinks nothing of killing men who think they are his friends, and their children (or wives).  He works with villains like the murderers because he does not want to get his hands dirty himself.  All he cares about is maintaining his throne now that he has it.

Macduff is with Malcolm when he learns what happened to his family.  He is horrified that he lost all of his family at one time.

All my pretty ones?
Did you say all? O hell-kite! All?
What, all my pretty chickens and their dam
At one fell swoop? (Act 4, Scene 3)

Malcolm tells him to “Dispute it like a man,” which basically means he has to fight Macbeth, and in that way he will accomplish their goal and avenge his family.  Macduff actually manages to hold it together pretty well. The witches have told Macbeth that he needs to beware Macduff, but they also said no man born of woman could hurt him.

When Macduff meets Macbeth in battle, he tells him that he was “from his mother's womb/Untimely ripp'd” (Act 5, Scene 8).  This subdues Macbeth, who gives up hope from then on.  Macduff beheads him, and Malcolm takes his spot as king.