"Seems, madam? Nay, it is. I know not “seems”.
Gertrude has asked why Hamlet's grief for his dead father SEEMS so strong in him. He answers bitterly that he is incapable of pretending. He begins the drama by demonstrating that he must be honest in his grief.
Ironically he must be dishonest throughout the rest of the play as he executes the orders of the ghost.
There is a noticable absence of a warm nurturing chat between mother and son as he seems to unravel into insantiy. Meanwhile Polonius, though a fraud, has a reasonbly warm relationship with his children.
It can be said that Hamlet seems preoccupied with his mother's sexuality. He rages as much about the incest as he does the murder, perhaps even moreso. The ghost of his father tells him to leave his mother to God and pursue Claudius but he just can't help himself. He would prefer to torture Gertrude over her... warm bloodedness.
...seriously, what a great play.
The relationship between Hamlet and his mother is a complicated one and somewhat open to interpretation. In Act 1, sc, 2, Hamlet and his mother are close enough that he can insinuate insults to her. He calls her "common", sarcastically calls her "good mother". In his soliloquy in that scene, he says of Gertrude, "frailty, thy name is woman". He's clearly frustrated with his mother and feels betrayed by her rapid marriage to her brother-in-law. In Act 2, sc. 2, Gertrude says that she feels the reason for Hamlet's recent odd behavior is her marriage to Claudius, indicating that due to the closeness of the relationship she formerly had with Hamlet, she knows that the marriage upset Hamlet. Later, in Act 3, sc. 4, when Hamlet goes to see his mother in her chamber after the play and Claudius's reaction to it, the words exchanged between the two of them further suggest that there was a close relationship between Gertrude and Hamlet. Again he feels free to insult her such as when he says, "And (were it not so) you are my mother." By the end of this scene, the two have reconciled and Gertrude asks Hamlet for advice as to what action she should take.