We read in the Bible such expressions as these: 

“The soul that sinneth, it shall die” (Ezekiel 18:4) and “Every soul that will not hear the voice of that Prophet shall be destroyed from amongst the people (Acts 3:23). These contradict the idea of everyone having an immortal soul that cannot die. This idea is of heathen origin and nowhere taught in the Bible

Genesis 2:7 gives the scriptural definition of the soul. “And the LORD God formed man of the dust of the ground and breathed into his nostrils the breath of life and man became a living soul.”  Adam did not receive a soul; he became a soul. Thus, Soul = Body + Breath of Life. When the breath of life is gone, the soul ceases. Ecclesiastes 3:19-20 (BBE), “the fate of the sons of men and the fate of the beasts is the same. As is the death of one so is the death of the other, and all have one spirit…All go to one place, all are of the dust, and all will be turned to dust again.”

However, Jesus’ sacrifice guarantees that all will be ransomed from the grave in the resurrection. “Who (Jesus) gave himself a ransom for all to be testified in due time.,” 1 Timothy 2:6.  

1 Corinthians 15:22 further explains, “As in Adam all die, even so in Christ shall all be made alive.” The resurrection is mankind’s only hope for a future life. As Martha said to Jesus, “I know that he (Lazarus) will rise again in the resurrection on the last day,” John 11:24.

So, what does happen when a person dies? Jesus used the word “sleep” as a synonym for “death.” When Lazarus died, Jesus said, “Our friend Lazarus has fallen asleep,” John 11:11. Again in Acts 13:36, “Now David…fell asleep.” Ecclesiastes 9:10 further explains, “there is no work, nor device, nor knowledge, nor wisdom in the grave whither thou goest.” 

Immortality is conditional. Immortality is also a reward given to Christians who are faithful and obedient. “Be thou faithful unto death, and I will give thee the crown of life,” Revelation 2:10. (See also 1 Corinthians 15:53,54 and 2 Peter 1:4.)

Additional Resources:
Christian Questions Podcast
Episode #1227: “Where Do the Human Soul and Spirit Go When We Die? (Part I)”
Defining what the human soul is and is not, and its destiny at death
Preview Video
CQ Rewind Show Notes

Episode #1228: “Where Do the Human Soul and Spirit Go When We Die? (Part II)”
Defining what the human spirit is and is not, and its destiny at death
Preview Video
CQ Rewind Show Notes

Blog Post: What is the difference between the soul and the spirit?

For children, parents and Bible class teachers:
Animated video: What is the soul?