Summary: Christ bringeth to pass the resurrection of all men—The righteous dead go to paradise and the wicked to outer darkness to await the day of their resurrection—All things shall be restored to their proper and perfect frame in the resurrection. About 73 B.C.
This is an interesting chapter; it chronicles what happens to us after we die. If only everyone who has asked this question (probably almost everyone who has lived) could read this and understand part of the immediate afterlife.
The institue manual had a lot of interesting information about this chapter, so I used a lot of it here. Don't feel like you need to read all of this, but it was helpful to me to break the chapter down into sections.
Verses 6-10 discuss God's Time.
Alma said that he did not know if there was more than one time appointed for the resurrection of men, but that it did not matter because "all is as one day with God, and time only is measured unto men."
Our Father in Heaven has a different perspective of time than we do here in mortality. The Prophet Joseph Smith revealed that where God dwells all things “are manifest, past, present, and future, and are continually before the Lord” ( D&C 130:7) The Prophet also said that the Lord “contemplated the whole of the events connected with the earth, pertaining to the plan of salvation, before it rolled into existence or ever ‘the morning stars sang together’ for joy; the past, the present, and the future were and are, with Him, one eternal ‘now’” ( Teachings of the Prophet Joseph Smith, p.220).
Verses 11-15 talk about death and resurrection.
Vs. 12 says, "The spirits of the righteous are received into a state known as paradise: “a state of happiness, ... a state of rest, a state of peace, where they shall rest from all their troubles and from all care, and sorrow"
Orson Pratt has this to add:
"When our spirits leave these bodies, will they be happy? Not perfectly so. Why? Because the spirit is absent from the body; it cannot be perfectly happy while a part of the man is lying in the earth. How can the happiness be complete when only a part of the redemption is accomplished? You cannot be perfectly happy until you get a new house. You will be happy, you will be at ease in paradise; but still you will be looking for a house where your spirit can enter, and act as you did in former times, only more perfectly, having superior powers. Consequently, all the holy men that have lived in days of old, have looked forward to the resurrection of their bodies; for then their glory will be complete" (in Journal of Discourses, 1:289–90).
Verses 16-22 discuss the First Resurrection.
Alma was unsure about the order of the Resurrection, but he gave it as his opinion that "the souls and the bodies are reunited, of the righteous, at the resurrection of Christ, and his ascension into heaven."
"While there was a general resurrection of the righteous at the time Christ arose from the dead, it is customary for us to speak of the resurrection of the righteous at the Second Coming of Christ as the first resurrection. It is the first to us, for we have little thought or concern over that which is past. The Lord has promised that at the time of his Second Advent the graves will be opened, and the just shall come forth to reign with him on the earth for a thousand years....
"Following this great event, and after the Lord and the righteous who are caught up to meet him have descended upon the earth, there will come to pass another resurrection. This may be considered as a part of the first, although it comes later. In this resurrection will come forth those of the terrestrial order, who were not worthy to be caught up to meet him, but who are worthy to come forth to enjoy the millennial reign...."
(Joseph Fielding Smith, Doctrines of Salvation, 2:295–97).
Verses 23-25 talk about the Resurrection:
"... What else would satisfy us? What else would satisfy the desire of the immortal soul? Would we be satisfied to be imperfect? Would we be satisfied to be decrepit? Would we be satisfied to remain forever and ever in the form of infirmity incident to age? No! ... From the day of the resurrection, the body will develop until it reaches the full measure of the stature of its spirit, whether it be male or female." (Joseph F. Smith, Gospel Doctrine, pp.23–24).
And of course, there are the Sons of Perdition verse 26 talk about. Bruce R. McConkie has an interesting statement to add to this verse:
"Eventually, all are redeemed from spiritual death except those who have ‘sinned unto death’ ( D.&C. 64:7 ), that is, those who are destined to be sons of perdition. John teaches this by saying that after death and hell have delivered up the dead which are in them, then death and hell shall be ‘cast into the lake of fire. This is the second death .’ ( Rev. 20:12–15 .) And thus the Lord said in our day that the sons of perdition are ‘the only ones on whom the second death shall have any power’ ( D.&C. 76:37 ), meaning any power after the resurrection” ( Mormon Doctrine, p.758). "
(and the institute manual)