Helaman 14

As Samuel, a Lamanite, prophesied the death of the Savior, he teaches -

"...this death bringeth to pass the resurrection, and redeemeth all mankind from the first death—that spiritual death; for all mankind, by the fall of Adam being cut off from the presence of the Lord, are considered as dead, both as to things temporal and to things spiritual.
17 But behold, the resurrection of Christ redeemeth mankind, yea, even all mankind, and bringeth them back into the presence of the Lord.
18 Yea, and it bringeth to pass the condition of repentance, that whosoever repenteth the same is not hewn down and cast into the fire; but whosoever repenteth not is hewn down and cast into the fire; and there cometh upon them again a spiritual death, yea, a second death, for they are cut off again as to things pertaining to righteousness.
19 Therefore repent ye, repent ye, lest by knowing these things and not doing them ye shall suffer yourselves to come under condemnation, and ye are brought down unto this second death."  (Book of Mormon | Helaman 14:16 - 19)

Thus the first death was the consequence of the fall of Adam bringing about both physical and spiritual death.  The Savior's atonement overcomes both for all mankind.  But there is a second death for those that will not repent and keep His commandments.  This death is eternal.