a woman who has moved on with her life. After her husband,King Hamlet, died, she had found her way to Claudius within a couple of weeks. Her reasons for moving on so quickly have long been a point of debate for literary scholars, with some believing she could have had a role in the murder and others pointing to the societal context of living as a former queen in this society, noting that perhaps Gertrude was simply trying to save her own life.

Regardless of her reasoning, Gertrude did move on, and she quickly begins building a new future for herself with Claudius. Here, she is telling Hamlet that he must do the same. Looking for his "noble father in the dust" is a pointless endeavor for Gertrude, who instead chooses to build her future in Denmark by creating new opportunities for herself.

Gertrude reminds her son that "all that lives must die," or that circumstances are forever changing. In these lines, she is steadfast in her resolve to keep moving forward through the trials of life, influencing her own circumstances to her favor as much as she possibly can.

In this passage from Hamlet, Gertrude prevails upon her son to move beyond his mourning period—"Cast thy nighted colour off"—and accept the changing situation. She argues that it is not as if anything out of the ordinary has happened—"thou know'st tis common"—and that Hamlet should not "forever . . . seek for thy noble father in the dust."

On the surface, Gertrude's words are simply an appeal to a son she knows to be given to melancholy and over-thinking ("seek"ing), but the word "common" here is one that was also often used to suggest a "regular" way of death—as in, death by natural causes, as opposed to by murder. So, Gertrude is attempting to forestall any thoughts on Hamlet's part that there was anything uncommon or unnatural about the manner of his father's death. She also begs him to "look like a friend upon Denmark."

Hamlet responds that it (death) is indeed common, but rejects the idea that this should mean he is content with the situation. He says he has "that within which passeth show"—that is, he harbors a grief deeper than whatever can be shown by the trappings of mourning, as performative grief. There is an implication here that he thinks the grief of others may be only "show." He believes that his mother has moved on too quickly from his father and that the whole situation is, as we will discover more throughout the course of the play, somehow sinister in his mind.

Gertrude is not only encouraging Hamlet to accept the death of his father, the former King, but perhaps more important, in the lines

And let thine eyes look like a friend of Denmark./Do not for ever with they vailed lids/Seek for the noble father in the dust. . . .

she is telling Hamlet to accept the fact that Claudius is the country's new king--Claudius, like Hamlet's father before him, is now "Denmark"-- and as such, deserves Hamlet's support.  Implicit in her statement is the concept of feudal, as well as family, obligations to which Hamlet must adhere.  And given Shakespeare's skill with and love of wordplay, Gertrude's reference to Hamlet's "vailed lids" may be a subtle acknowledgement that veiled lids indicate disguised motivations rather than constitute merely a physical expression of mourning.

The importance of Hamlet's situation is clear in his next speech to his mother when he answers her question, "why seems it [his grief] so particular with thee?"  Hamlet points out that the trappings of grief are just that, but his grief goes much deeper than the outward manifestations suggest:

. . . These indeed seem,/For they are the actions that a man might play;/But I have that within which passeth show--/These but the trappings and the suits of woe.

Given Hamlet's suspicions about his father's death at Claudius's hands, it seems reasonable to believe that Hamlet is both describing the depth of his grief here and pointing out that perhaps the grief of others, most notably, Claudius, is characterized only by "trappings and the suits of woe."

Queen Gertrude instructs Hamlet to "cast thy nighted color off" in Act I, scene two.  Gertrude and Claudius both approach Hamlet after Claudius' announcement that he has married Hamlet's mother. 

Hamlet is visibly upset at this news, so Gertrude attempts to pacify him, telling him to "cast thy nighted color off and let thine eye look like a friend on Denmark" (I.ii.70-71).  The meaning of these lines are two fold. First, Gertrude does not wish for Hamlet to pout angrily about the news; she  wants him to be more friendly to the new king.  "Cast thy nighted color off" also suggests black, the color of mourning, and that Hamlet most likely was dressed in black.  Gertrude wants Hamlet to be able to look past the tragedy of his father's death and see the potential of the future.

"Seek for thy noble father in the dust.

Thou know’st ’tis common. All that lives must die,

Passing through nature to eternity" (I.ii.73-5).