Okay, you asked. I'll answer your question, but be forewarned, brevity is an art I have never quite mastered.
We believe that the human spirit is eternal. That means that it not only will continue to exist forever but that it existed before we were born and resided in God's presence. A spirit is a cognizant entity, capable of feeling, thinking, learning, judging and making a choice between various options. A spirit can exist apart from a physical body or it can inhabit a physical body. Our spirits (yours, mine, everybody's) existed apart from our physical bodies before we were born. They entered into our physical bodies either at birth or at some point after conception (if my Church has any specific doctrine on the exact time, I'm unaware of it). When we die, our spirit leaves our body but does not cease to exist. It continues to be exactly the same entity as it was prior to our birth and during our mortality. An inquisitive, thoughtful spirit has always been an inquisitive, thoughtful spirit and will always continue to be. On the flip side, a judgmental, cynical spirit carries these same traits through its eternal existance. So, the spirit -- the real essence of who a person is -- continues to exist after death.
If it continues to exist after death, where does it go? We believe it goes to the "Spirit World." This is essentially the same place some of the ancient religions referred to as Hades. It's not so much a place as it is a state of mind. For the righteous, this state can be best described as "Paradise." It is a state of peace, rest and happiness. Jesus Christ told the repentant thief who hung next to Him on the cross that He would see Him that same day (the day they both died) in Paradise. We don't know a whole lot about that man. Presumably, Jesus did. He could see the condition of the man's heart and responded accordingly. For the wicked, death is the entrance into a state resembling "Prison." Again, it's not an actual place, because a spirit cannot be confined to a place. It is, rather, a state of mental torment, anguish and overwhelming sadness.
The Bible mentions both of these realms. As I already stated, we know that Jesus visited Paradise on the day He and the repentant thief died, and met the man there. When Mary saw Him in the Garden on Easter morning, He told her not to touch Him because He had not yet ascended to His Father in Heaven. Right there we have an important clue that Paradise and Heaven are not one and the same. There is also a mention of His visit to the spirits in prison. He spent three days teaching them (He also being in spirit form) while His body lay in the tomb. It would be inconceivable to think that He taught them His gospel only to conclude by saying, "Too bad you didn't hear it while you were mortal beings. You're out of luck now." No, He taught these spirit beings and allowed them to accept or reject His message. Those who accepted it and repented of their sins would be released from their state of suffering and be permitted to know the same joy and peace as those in Paradise.
Almost all of traditional Christianity accepts the fact of His visit to the Spirit World, even if they do not call it by that term. What they don't believe is that it still exists today, even though there is no biblical evidence that it has ceased to exist or that there is not still a need for it. We believe that the work of spreading the gospel of Jesus Christ continues today in the Spirit World, and that those who have accepted the message of redemption are spreading the word to those who haven't. Undoubtedly, there are many non-Christians who are already in Paradise. They are a step ahead of those who are in the Spirit Prison, but they also would need to hear and accept the sacrifice Jesus Christ made for them. The gospel is being taught in the Spirit World to hundreds of thousands of spirit beings every day. It will continue to be taught until the spirit of literally every person who has ever lived has heard and had the opportunity to accept the message.
This missionary work in the Spirit World is what Jesus was referring to when He said that the gates of hell would not prevail against His Church. To the Apostles who heard Him say this, the phrase "the gates of hell" would not have conjured up some sinister meaning Christians today understand it to mean. They would have understood "the gates of hell" to mean nothing more than the entrance to the world of departed spirits, and would have known from this that even death could not stop the spreading of His gospel.
Billions of people have lived and died without having ever heard the gospel of Jesus Christ. Billions more have perhaps heard it but, due to circumstances beyond their control, did not fully understand it. People are living today in places throughout the world where the laws of the land would prohibit them to convert to Christianity even if they wanted to. We all look at spiritual truths from different perspectives and, to one extent or another, we all carry around cultural, emotional, political, intellectual, etc. baggage. We will shed this baggage in the Spirit World. Our spirits will not have changed in any way (i.e. some people will be receptive to the message while others will not), but we will be able to see things more clearly. Those who truly want to know the truth will be able to recognize it when they hear it.
By the time we all stand before God to be judged, not one soul will be able to say, "I would have chosen Jesus Christ had I only known about Him." All will have played on an equal playing field for a period of time sufficient to allow them to make an informed choice. At that time, all of the dead will resurrect. The spirits awaiting the resurrection will be reunited with their newly perfected, immortal bodies and will be received into either Heaven or Hell (aka "Outer Darkness"). We believe that the vast, vast majority will end up in Heaven. Only a tiny number will want nothing to do with God. I personally expect to see not only many of my LDS friends in Heaven, but also many of my Catholic, Jewish, Muslim, Buddhist and
even atheist friends there.
Now, are you sorry you asked? And will you be nice in the future?