What Happens to Us When We Die?
The Bible gives us some information about this question.
1 Corinthians 15:51-52
[Paul:] Listen, I am telling you a mystery: We will not all fall asleep, but we will all be changed, in a moment, in the twinkling of an eye, at the last trumpet. For the trumpet will sound, and the dead will be raised incorruptible, and we will be changed.
Let's use a simple example to explain this. When we fall asleep at night, say at 11pm. Then we wake up thinking we did not sleep much, but when we look at the clock, it's 4am!! How did 5 hours pass and we did not feel them? This is the exact phenomenon Paul is talking about. It is about what it will feel like, between the moment we die and the moment we hear the trumpet on Judgement day. It may be thousands of years later, but to the person who just died, it'll feel like a moment, a "twinkling of an eye"!
Then the next question becomes, what happens to the person during the in-between time? The Bible says, the person's spirit will be with God, awaiting judgement:
and the dust returns to the ground it came from, and the spirit returns to God who gave it.
2 Corinthians 5:8
[Paul:] We are confident, yes, well pleased rather to be absent from the body and to be present with the Lord.
Notes: So at death, all people's spirits whether good or bad return to God, while the body on earth decays. God keeps our spirit with Him until judgement day. He will then place our spirit in our refashioned risen body, including our memories and personality - so that our individuality is retained.
Knowing this, it should be comforting to people when they lose a loved-one. This is why the Bible says, don't mourn like pagans do - screaming like crazy:
1 Thessalonians 4:13-14
We do not want you to be uninformed, brothers and sisters, concerning those who are asleep, so that you will not grieve like the rest, who have no hope. For if we believe that Jesus died and rose again, in the same way, through Jesus, God will bring with him those who have fallen asleep.