Hamlet's dilemma is that he is on the line whether or not to kill himself over this issue that has come up with his uncle. He recently had to deal with his father dying and his uncle marrying his mother and now the ghost of his father is telling him his uncle killed him. Hamlet wants to obey his father but at the same time he wants to get rid of all the stress that this brings. He reflects on why people would suffer this life and concludes that they are afraid of the unknown. "But that the dread of something after death. The undiscovered country from whose bourne no traveler returns."
Hamlet has already set up plans for his uncle and is committed to killing him. Hamlet pretty much already made up his mind that he will not kill himself. He decides that he will choose to live and avenge his father rather than take the easy way out and die. He decides this because he is afraid of death and also loves and respects his father. His uncle married his mother only about a month after his father died, therefore swaying Hamlet to kill him.
On the other hand that is a big task killing someone isn't easy and Hamlet doesn't know of he can handle the stress of it all. However, people deal with stresses similar to his own and they live it out because they fear the unknown. Hamlet takes this into account as well that so many decide to suffer on through life. He has something he must do so he ultimately decides to live.