Physical Death- Each and every one of us will suffer physical death. When our time on the earth has passed our life will end and our body and spirit will separate. The body will go the ways of the earth, being either buried or cremated or whatever you choose to have done to it. This is where the atonement comes in. When Christ was resurrected he let loose the bands of physical death. Thus all of us will like him, be resurrected when the time has come.
2Nephi 9:11 And because of the way of deliverance of our God, the Holy One of Israel, this death, of which I have spoken, which is the temporal, shall deliver up its dead; which death is the grave.
Spiritual Death- The other death that each of us will face is spiritual death, or the separation from our Father in Heaven. We suffer this death because of our sins. Every sin that we commit regardless of how small takes us away from our Father in heaven. Then there becomes this growing gap that must be bridged. The atonement of Christ is that bridge. Christ has suffered for our sins and paid the price so that we can be forgiven and remain in Gods presence, if we repent.
Alma 12:16 And now behold, I say unto you then cometh a death, even a second death, which is a spiritual death; then is a time that whosever dieth in his sins, as to a temporal death, shall also die a spiritual death; yea, he shall die as to things pertaining unto righteousness.
Alma 13:30 And may the Lord grant unto you repentance, that ye may not bring down his wrath upon you, that ye may not be bound down by the chains of hell, that ye may not suffer the second death.