What is a soul? Genesis 2:7, we read there that, "The Lord, God formed the man from the dust of the ground and breathed into his nostrils the breath of life." Notice what it says. It doesn't say God gave him a soul, it says man became a living soul. The combination of those two things together, he became a living soul. Now, when someone dies, the opposite of those two things happens.
In other words, before man becomes a soul, it's the elements of the earth that God combines with the breath of life, and he becomes those two things together equal a living soul. When you die, those two things are basically separated. You can read about that in Ecclesiastes 12:7, "Then the dust shall return to the earth as it was, and the spirit will return to God who gave it."
When a person dies, we know what happens to the body, ashes to ashes. I've said over many graves at a graveside service, the body will turn back into dust. Someone might ask, "But what about cremation?" That's just really exhilarating the same process. There are a couple of examples of saved people in the Bible who were cremated, like Jonathan, for instance, the son of Saul. We expect he'll be in the Kingdom.
Cremation does not disqualify you from the resurrection. Some people think that if you're buried, God can find all the parts and put you back together again, but if you're cremated, if they scatter the ashes, He will never be able to reassemble you. There are actually people who worry about this. It doesn't really matter, because the Bible says that everything is new, He's not using the old parts to reassemble you.