This is one of the most complex scenes in drama, and there are many ways of approaching each of the characters, but I am going to give you my take on it. Claudius and Polonius have sent for Hamlet in order to get him to meet with and talk to Ophelia who has been placed strategically in his path. They hope he will reveal some of his inner secrets. (Polonius is convinced that this secret is that Hamlet is in love with Ophelia; Claudius is not so sure) Hamlet has guessed from the summons what Claudius is trying and so is aware that he is behind the tapestries. However, Hamlet does not know that Ophelia is aware of what Claudius is doing, nor that Polonius knows and has revealed to Claudius the nature of their relationship. He does not think that Ophelia is up to the mental and emotional strain of the intrigue at the Danish court, and wants her to get out of the way so she won't get hurt. Ophelia is of course aware that Claudius and Polonius are lurking in the curtains, but she believes that Hamlet is mad at her because, on her father's orders, she has given Hamlet the cold shoulder. She wants Hamlet to know she still loves him, but also wants to convince the eavesdroppers that she is still playing aloof. You see what I mean about complicated.
So the scene commences and Hamlet, trying to persuade Ophelia to get herself out of the court, advises her to go to a nunnery, which at first means a convent. We know this is what he means because he asks "Why wouldst thou be a breeder of sinners?" and nuns do not breed sinners. But something happens around the line "Where is your father?" and Ophelia's answer, which is a lie and which Hamlet can tell is a lie, reveals to him that Ophelia is already involved and has agreed to help Claudius in his spying. After this the "nunnery" becomes a brothel, and Hamlet charges her with every form of insincerity and betrayal. His "get thee to a nunnery" becomes a disgusted dismissal. Ophelia is hurt by the fact that she is repudiated by Hamlet, terrified by his behaviour, and confused. She grasps at the simple that he must be crazy to behave like this, as becomes apparent in her speech "O, what a noble mind is here o'erthrown!
