I think I understand your question, but not fully. Here is my answer based on my understanding. You asked: "Because of Christ's death, what does death mean for me?"
Christ felt everything we have gone through (joy, pain, sorrow, etc), and suffered for it in the Garden.
Alma 7:11-12 Book of Mormon
11 And he shall go forth, suffering pains and afflictions and temptations of every kind; and this that the word might be fulfilled which saith he will take upon him the pains and the sicknesses of his people. 12 And he will take upon him death, that he may loose the bands of death which bind his people; and he will take upon him their infirmities, that his bowels may be filled with mercy, according to the flesh, that he may know according to the flesh how to succor his people according to their infirmities.
He died on the cross for us and decended below all things so he could feel our pain, so he would know how to succor us:
Doctrine and Covenants 19:15-19
15 Therefore I command you to repent—repent, lest I smite you by the rod of my mouth, and by my wrath, and by my anger, and your sufferings be sore—how sore you know not, how exquisite you know not, yea, how hard to bear you know not. 16 For behold, I, God, have suffered these things for all, that they might not suffer if they would repent; 17 But if they would not repent they must suffer even as I; 18 Which suffering caused myself, even God, the greatest of all, to tremble because of pain, and to bleed at every pore, and to suffer both body and spirit—and would that I might not drink the bitter cup, and shrink— 19 Nevertheless, glory be to the Father, and I partook and finished my preparations unto the children of men.
So what does His death mean for us? It means that we can repent and become clean again as Isaiah promised
18 Come now, and let us reason together, saith the LORD: though your sins be as scarlet, they shall be as white as snow; though they be red like crimson, they shall be as wool.
Now as pertaining to what happens to your spirit once you die, the best scriptural account I have read is from The Book of Mormon in Alma 40
11 Now, concerning the state of the soul between death and the resurrection—Behold, it has been made known unto me by an angel, that the spirits of all men, as soon as they are departed from this mortal body, yea, the spirits of all men, whether they be good or evil, are taken home to that God who gave them life.
12 And then shall it come to pass, that the spirits of those who are righteous are received into a state of happiness, which is called paradise, a state of rest, a state of peace, where they shall rest from all their troubles and from all care, and sorrow.
13 And then shall it come to pass, that the spirits of the wicked, yea, who are evil—for behold, they have no part nor portion of the Spirit of the Lord; for behold, they chose evil works rather than good; therefore the spirit of the devil did enter into them, and take possession of their house—and these shall be cast out into outer darkness; there shall be weeping, and wailing, and gnashing of teeth, and this because of their own iniquity, being led captive by the will of the devil.
14 Now this is the state of the souls of the wicked, yea, in darkness, and a state of awful, fearful looking for the fiery indignation of the wrath of God upon them; thus they remain in this state, as well as the righteous in paradise, until the time of their resurrection.
15 Now, there are some that have understood that this state of happiness and this state of misery of the soul, before the resurrection, was a first resurrection. Yea, I admit it may be termed a resurrection, the raising of the spirit or the soul and their consignation to happiness or misery, according to the words which have been spoken.
I hope I understood your question correctly, if not, please clarify and I will see if I can answer differently.