Hamlet has been hesitant in carrying out his revenge against
Claudius, putting it off until he can know for sure that Claudius
is guilty. He accidentally kills Polonius, making Hamlet feel
God is using him as a tool of vengeance to punish Polonius not only
for his sins, but to also punish Hamlet for his own sins. Killing
Polonius leads Hamlet to look at it in terms of retribution,
punishment, and vengeance when he says, "Heaven hath pleased it
so/To punish me with this, and this with me."
Now that Hamlet has killed Polonius, he will be considered truly
mad by everyone. His mother certainly believes he is, and he will
lose Ophelia because of his mistake in thinking Claudius was behind
the curtain. After this act, Hamlet has nothing else to lose. It
marks the loss of everyone who is important to him, his father,
mother, and Ophelia. Though Hamlet doesn't achieve his vengeance
with the death of Polonius, he knows now that he can committ murder
and carry out his vengeance against Claudius.