What does Luke 16:24 mean?
A rich man is in Hades: the temporary place of the unsaved dead before final judgment. The poor, starving, afflicted beggar he ignored outside his gate is now in paradise, comforted by Abraham (Luke 16:19–23). The rich man begs Abraham to send the once-beggar, Lazarus, to ease his pain.The rich man calls out for "Father Abraham." He is a Jew, a physical descendant of Abraham. It was through Abraham that God chose His people. At that time, it was normal for Jews to assume they were God's people because of their ethnicity. John the Baptist vehemently rejected this. Those who are spiritual descendants of Abraham naturally do good works (Luke 3:8–9). The rich man ignored Lazarus, letting him die in the streets.
The rich man, interestingly, doesn't argue about his place in Hades. He makes no attempt to argue that he deserves a different fate. Yet he is longing for relief and treats Lazarus as a servant to get it. Scripture doesn't indicate whether the man sees the irony in the situation. He wants Lazarus to cross a great chasm to give him a bit of water (Luke 16:26) although the wealthy man wouldn't walk out his own gate to give Lazarus the crumbs to keep him alive (Luke 16:19–21).
The story of the rich man and Lazarus is odd and doesn't seem to be a "parable." A parable is a story about everyday life that has a spiritual, metaphorical meaning. Of all the parables Jesus tells, none of them name any of the characters like this one does. That leads some scholars to suggest this is a true story. Do angels take the righteous dead to paradise? Does Abraham welcome God-following Jews when they die (Luke 16:22)? Can the dead in paradise and Hades see each other (Luke 16:23)?
Some of the details are confirmed in other places. Jesus says that those who go to Hades will be able to see "Abraham and Isaac and Jacob and all the prophets in the kingdom of God" (Luke 13:28). The Old Testament (Isaiah 66:24), New Testament (Mark 9:48), and extra-biblical Jewish writings mention the unsaved will be tormented as if by fire. There's every reason to believe that the dead in paradise and the dead in Hades cannot change their location. Other than that, it's unwise to cling tightly to too many of the details of this passage.