How does act four help to further the plot? Explanation and examples.

Act IV is pivotal to the play's plot because it shows the
consequences of Hamlet's plan to flush out Claudius as his father's murderer.  First of
all, Hamlet has orchestrated a play that so mimics his father's murder that Claudius,
through his actions and overheard confession, has admitted his crime.  Second, Hamlet's
has killed Polonius, his girlfriend's father, while arguing with this
mother.

The consequences of these actions are astounding. 
First, Gertrude must choose between her son and her husband.  She chooses her son when
she confirms to Claudius that Hamlet is crazy.  She
notes,

Mad as
the sea and wind, when both contend

Which is the mightier;
in his lawless fit,

Behind the arras hearing something
stir,

Whips out his rapier, cries, 'A rat, a
rat!'

And in this brainish apprehension,
kills

The unseen good old
man."

While this murder draws
Claudius' attention away temporarily, Ophelia, his girlfriend goes crazy and commits
suicide while her brother Laertes returns looking for blood.  This quest eventually
leads to Hamlet's death as well.

Claudius sends Hamlet away
with the point of having him killed, but Hamlet thwarts this plan only to return to
another, more fatal deception.

Act Four provides the
consequences for Hamlet's actions in Act III and sets up the final act in which all the
principal characters die.