In "Hamlet" what is the reason of Hamlet's mother's marriage?
We never really get any reason. She just did. The story doesn't focus on her motives; she has no monologues or conversations that would reveal why she married so quickly after her first husband's death. The play instead focuses on the fact that Hamlet finds it "wicked" and "incestuous", and through it, all women to be frail and fickle. Hamlet is so upset by this that he rants and raves at Ophelia, cutting off all contact with her, either in a sincere gesture of disgust at women, or in an indirect insult towards his mother, hoping that she will get the message. He lectures his mother in her rooms later on in the play, and condemns her for her actions.
The queen's motivation for marriage are not stated. Perhaps it was loneliness and practicality; she counsels Hamlet in the beginning to move past his father's death, "that lives must die, passing through nature to eternity" (I.ii.72-3). So, if she has taken her own advice, she is trying to move on and accept death as a natural course of things. But the point of the play isn't why she did it, just that she did, and it provides good fodder for Hamlet's angst with the world.