People often confuse the fact that Adam and Eve fell, and that we are thus guilty, too. No. We are not going to be punished for what they did. We are punished for our own sins. (Article of Faith 2). The Fall put them from an immortal state to a mortal state, one in which they could bring children into this world. It put them in a position where they and subsequently their posterity could be tried and tested in order to prove to our Father and to our Savior that we could be obedient to the commandments we have been given.
Always loved the scripture in the Book of Mormon, which sums up the truth of the Fall:
"Adam fell that men might be, and men are that they might have joy." (2 Nephi 2: )
But to dispel what people get wrong about it, there are the rest of the verses in that chapter (2 Nephi 2:19-27, emphasis added):