In Act 1 scene 3 of Hamlet, what does Polonius say to Ophelia about Hamlet?
Polonius plays the role of jealous and possessive father in this scene. He is very suspicious of any promise Hamlet has made to his daughter, and urges Ophelia to remember that as prince, he is able to do things and say things that she is unable to do. He urges her to disregard any vows and promises that he has made to her, as he feels that any such vows and promises are made without true sincerity and only have the objective of trying to take Ophelia's virginity. Note what he says about Hamlet and how Ophelia differs from him:
For Lord Hamlet,
Believe so much in him, that he is young,
And with a larger tether may he walk
Than may be given to you.
It must be remembered at this time that an unmarried woman's worth was based on her virginity, and that if this was taken, her status would drop accordingly. Polonius therefore appears to be very strict when he rebukes Ophelia in this scene, but he can also be seen as doing what he has to in order to protect his daughter and make sure she can marry one day and live a happy life in Danish society.
Polonius says that Ophelia has been to free with him. He criticizes their relationship and says that Hamlet does not truly love her, he is just young and impulsive, his professed love will soon come to pass. Polonius is saying that Ophelia is being naive, and cannot be with Hamlet anyways, as he is a prince and he is just toying with her so she should communicate less with him and be careful so she (and her father) does not lose her honor.