Hamlet has spent much of the play thus far trying to determine whether to believe the ghost claiming to be his father who has made claims that Claudius murdered him.
In this soliloquy, Claudius confesses everything, and Hamlet is within earshot. He feels intense guilt for his crimes and ponders aloud,
What if this cursèd hand
Were thicker than itself with brother’s blood?
Is there not rain enough in the sweet heavens
To wash it white as snow. (III.iii.46-49)
Hamlet has his answer. Claudius's hands are covered in his brother's (who is therefore Hamlet's father) blood and he questions whether heaven can wash these sins "white as snow" or if he can possibly be forgiven since he still retains all that he gained by committing the murder. His confession further acknowledges his motives:
I am still possessed
Of those effects for which I did the murder:
My crown, mine own ambition, and my queen. (III.iii.56-58)
Claudius wanted the crown, wanted Queen Gertrude as his own, and sought to fulfill his own ambition...
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