Gertrude is a complicated character in William Shakespeare's Hamlet, mostly because we do not ever really know the complete truth about what role she played in her first husband's death. We have clues throughout the play about her, but the first time anyone talks about her is in a monologue in Act I scene ii.
Here Hamlet explains why he is so upset at his mother; we knew he was angry, but until this soliloquy we did not know why. He explains that his mother remarried less than two months after her husband died--to her dead husband's brother.
Must I remember? why, she would hang on him,
As if increase of appetite had grown
By what it fed on: and yet, within a month--
Let me not think on't--Frailty, thy name is woman!--
A little month, or ere those shoes were old
With which she follow'd my poor father's body,
Like Niobe, all tears:--why she, even she--
O, God! a beast, that wants discourse of reason,
Would have mourn'd longer--married with my uncle,
My father's brother, but no more like my father
Than I to Hercules: within a month:
Ere yet the salt of most unrighteous tears
Had left the flushing in her galled eyes,
She married. O, most wicked speed, to post
With such dexterity to incestuous sheets!
We learn that she acted as if she loved King Hamlet more than anything, and the king certainly did love Gertrude. Then, of course, she marries her brother-in-law. Hamlet's feelings about Claudius are clear, but he is no less clear about his disdain for his mother's choice of husbands and the haste with which she remarried.
A second important quote about Gertrude is found in the scene where Hamlet confronts he in her bedroom and makes her see the error of her ways, She finally begs him to stop his accusations and admits:
O Hamlet, speak no more:
Thou turn'st mine eyes into my very soul;
And there I see such black and grained spots
As will not leave their tinct.
The question is what, exactly, is she admitting to here? Is she just admitting that she "goofed" by marrying such a low man in such a hasty way, or is she admitting to something deeper, as in her role in King Hamlet's murder, either directly or indirectly. It is the key question of the play regarding Gertrude, and it remains unanswered.
Finally, in the last scene, Gertrude playfully but forcefully disobeys her husband's wishes and drinks from the poisoned cup. What she says is, "I will, my lord; I pray you, pardon me." If she is simply feeling a bit rebellious toward or perhaps even miffed at Claudius, that line is just a simple assertion of her autonomy. If, however, she is insisting on drinking from the cup in order to save her son from being poisoned, it is the ultimate sacrifice of a loving mother.
Gertrude is an intriguing and rather ambiguous character because her words and actions are open to so many interpretations.