The graveyard scene is a turning point for Hamlet - his thoughts and opinions on death become more solidified and he soon decides what he is going to do about his revenge and life in general.
During the graveyard scene, we see Hamlet holding Yorick's skull, who used to be his court jester. Hamlet is contemplating life and death, thinking about how it is odd that he used to know this skull while it still belonged to a living man, and that now he is gone, turned to dust.
He is also thinking about many famous people, such as Alexander the Great and Caesar, realizing that no matter how famous and accomplished you are, you are still inevitably going to die and turn to dust, as his friend, Yorick did. He used to be very torn about whether he should commit suicide or kill his uncle, and this is the very moment where he makes his decision after realizing that life is futile.
