Three things to say about this parable, which closes out this section (chapters 15-16) of parables we've said are focused on stewardship: First we must know the heart of the Father, then we can figure out how to appropriately manage our worldly goods in light of who God is.
1. This parable is often cited as some kind of evidence of what the afterlife is like. I've heard in-depth teachings using this parable to explain that when we die, we are taken to a sort of holding area. Those who are good / God-pleasing / righteous / saved will go to a pleasant place called "Abraham's bosom" and those who are bad / condemned / unrighteous / unsaved will go to a place of temporary torment called "Hades" or something similar. Please understand that mapping out the afterlife is NOT Jesus' point here. That would be a little like reading Moby Dick as a whaling manual or watching Jeremiah Johnson to figure out how to be a good trapper. Yes, that element is in the story, but it's not even close to the point. The Bible is frustratingly, intentionally fuzzy and vague about questions of exactly what happens in the afterlife. Many cultures surrounding biblical ones had extensive writings on this topic -- the Egyptian "Book of the Dead" is the best example -- so one has to think this omission is intentional. Think about it a bit, and you'll see that it must very well be so. God doesn't want you to trust some road map of where you're headed after you die. He wants you to trust him, in this life and the next. We are to be like Peggy who, a couple days before she died, told me, "I figure all I have to do is die, and Jesus will take care of the rest." Sound wisdom.
2. Having laid the foundation of revealing the Father's heart in chapter 15, Jesus is now making explicit his advice in the first part of 16: We are to use our worldly goods to please God. The rich man (interestingly unnamed, though tradition sometimes names him Dives) uses his abundant wealth to indulge himself, ignoring the beggar at his gate. The first point of the story is that this self-indulgence is clearly against God's desire, and eventually the rich man will experience the consequence of his selfishness. We are not called to be like the younger son in chapter 15, squandering our resources on our own lusts. Nor are we to be like the elder son, selfishly hoarding those resources and never allowing ourselves to live like we are heirs of the estate. Instead, we are to manage our goods as a reflection of the Father's heart, who cares for the outcasts, the sick, the marginalized, the orphan and the widow and the slave and the prisoner and the blind and the lame. The problem with the rich man is not that he is selfish, but rather that his selfishness puts him directly in opposition to the Father's heart.
3. The end of the parable is one of those intriguing statements that must have puzzled people when Jesus first uttered it but came to be extremely important in the early church. As the first Christians after Pentecost tried to tell their fellow Jews about Jesus and his resurrection, they faced tremendous frustration and disappointment and some limited success. Throughout the New Testament we hear echoes of that frustration, longing for the Jewish people to recognize Jesus as their Messiah. Here Jesus foretells that frustration, saying that even if someone rises from the dead (as he will shortly do) those who are entrenched in their own structures of religious power and certainty (the old wineskins he has talked about before) will refuse to believe him. We live with the same frustration today.
So don't let's make this a parable about the structure of the afterlife and miss Jesus' point. In regard to questions about what happens after death, maybe we are wisest to cling to Deuteronomy 29:29, where Moses tells the people that the hidden things belong to God, but the things that are revealed belong to us and our children forever. In Jesus' resurrection, the heart of the Father that will not even be stopped in the face of death is revealed and victorious. We cling to that.