Adam and Eve, the snake, and the Fall are all Biblical allusions found in the Book of Genesis in the Bible. In the Creation story of the Bible, God created Adam and Eve to enjoy paradise, the Garden of Eden; he gave them permission to rule over the garden and eat of any tree, except the tree of knowledge of good and evil (Genesis 2:17). In Chapter three of Genesis, the serpent tempts Eve to eat of the tree of knowledge, and she does; she also gives some to Adam to eat as well. But because Adam and Eve broke God's command not to eat of the tree of knowledge, they were punished and cast out of Eden.
These references to the story of Adam and Eve in Hamlet are significant, because the play deals with themes similar to the original Bible story--good versus evil, temptation, sin, punishment, a fall from grace.