In several passages the dead seem to be described as though they were asleep. For example, 1 Cor 15:6 says "Then he appeared to more than five hundred brothers at one time, most of whom are still alive, though some have fallen asleep." What does this mean?

In this passage Paul is saying that not all of the 500 Galilean witnesses to the resurrection are still alive. Obviously it would be silly to contrast being "still alive" with literally "fallen asleep," since the apostle is counting witnesses who can corroborate the claim that Jesus rose from the dead.

There are places passages in the Bible, particularly in the New Testament, where sleep is a metaphor for death. When this usage of sleep for death began, I do not know. (Anyone care to research and send in a blurb we could add to the A part of this Q&A?) But it's a common enough metaphor that we don't need to be confused about it. Here are some instances to consider:

  • Matt 27:52 -- The tombs also were opened. And many bodies of the saints who had fallen asleep were raised... (The NIV, which sometimes paraphrases -- changing words or phrases for clarity -- renders "fallen asleep" as "died.")
  • John 11:11 -- After he had said this, he went on to tell them, “Our friend Lazarus has fallen asleep; but I am going there to wake him up.” (Jesus is only stressing that the death is not final; Lazarus will soon "wake up.")
  • Acts 7:60 -- When he had said this, [Stephen] fell asleep. (Stephen has just been executed.)
  • 1 Cor 11:30 -- The physical punishments of sickness, weakness, and death befell some Corinthians who failed to discern the body of Christ in the Lord's Supper. (Paul couldn't have meant spiritual sickness, since that would be a tautology [As a result of failing to appreciate the body of Christ -- the spiritually sick and weak have become spiritually sick and weak].)
  • And many more scriptures, like Acts 13:36 (David); 1 Cor 15:18, 20; 15:51; and 1 Thess 4:14-15; 5:6, 10 (the general resurrection).

So we see that while not all sleep is death (fortunately!), all death can be described as "sleep."

Clarification: Acknowledging the well-evidenced metaphor -- admitting that "sleep" means death" -- is a far cry from admitting the doctrine of "soul sleep," which holds that the dead are in a state of mental oblivion. Many scriptures describe the dead as conscious (1 Sam 28:14-19; Matt 17:1-8; 2 Cor 5:6-8; Rev 6:10; Isa 14:9; Job 26:5 -- although poetic passages often include artistic license, hyperbolic speech, and other literary features that should caution us before we interpret them literally; and Luke 16:23-30 -- although this is a parable and should not be pressed too hard for post mortem doctrine) -- while others (like Ecc 9:5), based on an incomplete understanding of the afterlife (common throughout the O.T.), speculate that they are unaware of our world and somehow cut off from their relationship with God).