The main thing Laertes wants to know is who killed his father. The matter has been kept a mystery from the entire populace because Claudius, for Gertrude's sake, did not want it known that Hamlet is mad and that he committed the murder. This explains why the funeral of Polonius was conducted with great celerity and simplicity. There are other things Laertes wants to know about. When Claudius offers to give him a full explanation in the presences of Laertes' wisest friends, he tells Claudius:
Let this be so.
His means of death, his obscure burial—
No trophy, sword, nor hatchment o'er his bones,
No noble rite nor formal ostentation,
Cry to be heard, as 'twere from heaven to earth,
That I must call't in question.
By "hatchment" Laertes means a tablet bearing his father's coat of arms to be fastened to the front of his home and on his tomb after the funeral. It is evident that Laertes is largely angered by the neglect of the formalities and ostentation of mourning he feels his father deserves. The same will be true when his sister Ophelia is given a perfunctory burial ceremony because, as the Priest explains to Laertes the reason for what Hamlet calls "such maimed rites":
Her obsequies have been as far enlarged
As we have warranty. Her death was doubtful;
And, but that great command o'ersways the order,
She should in ground unsanctified have lodged
Till the last trumpet. For charitable prayers,
Shards, flints, and pebbles should be thrown on her.
Yet here she is allow'd her virgin crants,
Her maiden strewments and the bringing home
Of bell and burial.
By "great command o'ersways the order," the Priest means that the King has given order to give Ophelia the best funeral possible. The Priest believes that Ophelia committed suicide, which was a mortal sin.
Laertes' fury is intensified by what he regards as the outrageous treatment of both his dead father and his dead sister. The playwright's apparent purpose is to justify Laertes' consent to kill Hamlet in a treacherous manner when they have their fencing match. Laertes is a noble young man who would hardly consent to such an ignoble action under any other circumstances. The fact that the King himself suggests this treachery helps to persuade Laertes to go along with the scheme. Laertes is young and naive. He has no idea what a sinister and guilt-infested schemer he is dealing with in King Claudius.