In Act 1 of Shakespeare's Hamlet the Scene 2 is of great significance as it introduces the major conflict of the play. The scene establishes that Old King Hamlet has died recently and that his brother, Claudius, ascended to the throne and married his widow Gertrude quickly after his brother’s death.
Hamlet Act 1, Scene 2 begins with King Claudius of Denmark recapping recent events: his brother Old King Hamlet recently died, and Claudius married Old King Hamlet's widow Gertrude. He then sends messengers to the king of Norway, trying to convince him to dissuade his nephew Fortinbras (son of the deceased King Fortinbras) from invading Denmark.
Laertes, the son of Polonius (an adviser to the Danish throne) then gets Claudius's blessing to return to France to study. Claudius then addresses Hamlet, referring to him as "my cousin Hamlet and my son" and asks why "the clouds still hang on you." Hamlet responds flippantly, and Gertrude, his mother, advises him not to mourn his father for the rest of his life, because all living things die eventually. Claudius adds that it is commendable for Hamlet to mourn his father for a certain amount of time, "But to persevere/In obstinate condolement is a course/Of impious stubbornness." Claudius then declares that he loves Hamlet like a son, and grants permission for Hamlet to go back to Wittenberg to continue his studies. Gertrude, however, asks Hamlet to stay at home; Hamlet agrees to stay. Claudius claims to be pleased by Hamlet's decision; everyone exits except Hamlet.
Once he is alone, Hamlet delivers a soliloquy about his disgust that his mother married his uncle less than two months after his father's death. He reflects on how affectionate his father and mother were (or seemed) with one another, and compares his uncle unfavorably to his father.
To sum up, this scene represents Hamlet’s deep grief and sadness due to his father’s death and the events following it. He expresses his despair and disgust with his mother for remarrying so quickly after his father’s death. Hamlet’s anger to his mother is one of the central conflicts in the play, established in Act 1, Scene 2.