The play is really death-obsessed, as is Hamlet himself. As as A.C. Bradley has pointed out, in his very first long speech of the play, "Oh that this too solid flesh," Hamlet seems on the verge of total despair, kept from suicide by the simple fact of spiritual awe. He is in the strange position of both wishing for death and fearing it intensely, and this double pressure gives the play much of its drama.
One of the aspects of death which Hamlet finds most fascinating is its bodily facticity. We are, in the end, so much meat and bone. This strange intellectual being, which Hamlet values so highly and possesses so mightily, is but tenuously connected to an unruly and decomposing machine. In the graveyard scene, especially, we can see Hamlet's fascination with dead bodies. How can Yorick's skull be Yorick's skull? Does a piece of dead earth, a skull, really have a connection to a person, a personality?
Hamlet is unprecedented for the depth and variety of its meditations on death. Mortality is the shadow that darkens every scene of the play. Not that the play resolves anything, or settles any of our species-old doubts and anxieties. As with most things, we can expect to find very difficult and stimulating questions in Hamlet, but very few satisfying answers.