The second death, or spiritual death, is defined as being cut off from the presence of God. This means that you cannot see the face of God, you cannot withstand the presence of God, you will not enjoy the visitation of the Son, and you are not worthy of the smallest portion of the spirit of the Holy Ghost. It is a total and complete separation from God. As described in the scripture, this state happens to those who suffer in hell. It also describes the state of the Sons of Perdition who are cast out after the last soul is resurrected. Therefore, the second death has power upon all those who suffer in hell until the resurrection of the wicked. At that point the second death applies only to the Sons of Perdition, These are they who shall go away into the lake of fire and brimstone, with the devil and his angels—And the only ones on whom the second death shall have any power (DC 76:36-7).
One might be inclined to think that the “first death” must be the death of the mortal body. This is not the case. The Lord explains that the first death is also spiritual and occurs when we leave his presence and come to earth. This is symbolized by the fall of Adam, I, the Lord God, caused that he should be cast out from the Garden of Eden, from my presence, because of his transgression, wherein he became spiritually dead, which is the first death, even that same death which is the last death (or second death), which is spiritual, which shall be pronounced upon the wicked when I shall say: Depart, ye cursed (DC 29:41).