The Hebrew word ‘nephesh’ is translated by various related words – ‘soul’ (428 times), ‘life’ (119), ‘person’ (30), ‘heart’ (15), and ‘mind’ (15). Difficulties arise because, although the meanings are related, they are not exactly the same and even in those cases in which the word is translated as soul there is a range of meanings. In most cases it means a person. Thus, in Genesis 46:26 (KJV) we are told that Jacob took 66 souls with him when he went into Egypt, but it is obvious that this means 66 persons, and that is how it is translated in most of the newer versions. In Leviticus 5:1-4 (KJV) it speaks of a soul sinning, touching unclean things and swearing, and again it is clear that this refers to people doing these things, and the newer versions translate these verses to mean ‘anyone’ doing these things. Similarly, in Genesis 2:7 (KJV) we are told that the man became a living soul and the newer versions record that he became a living creature. In dozens of other cases soul simply means person.
However, when Rachel was giving birth to Benjamin, recorded in Genesis 35:18, it says (KJV and ESV) that her soul was departing. It is obvious that it was not her person that was departing, but her life. The NIV says that she breathed her last. In 1 Kings 17:22 (KJV) it says that, when a young lad was brought to life by Elijah, the soul of the child came into him again. It was the life of the child that came into him, and that is how it is translated in most of the newer versions.
In the New Testament, the Greek word that is translated as soul is ‘psyche’. This word is translated as ‘soul’ 58 times, ‘life’ 40 times, ‘mind’ 3 times and ‘heart’ once, so it is a close equivalent to the corresponding word in Hebrew. In Acts 27:37 there were 276 souls (KJV) or persons (ESV) on Paul’s ship. In 1 Corinthians 15:45 it says that the first Adam became a living being, which is exactly what Genesis 2:7 says. The same word, psyche is used by Jesus when he asks whether it is lawful to save life or to kill on the Sabbath (Mark 3:4). So the word sometimes means a person and sometimes means life — we depend on the context to decide which it is.
Jesus says that men can kill the body, but are not able to kill the soul. However, God who is able to kill both body and soul (Matthew 10:28). This means that God is able to destroy the life of the wicked, as he will do at the Day of Judgement, but no human can permanently destroy the life of the faithful who will be raised to eternal life.
There is no verse in the Bible that mentions immortal souls. In fact, in Ezekiel 18:4 it says, in all versions, that the soul who sins shall die. So the soul cannot possibly be immortal.