In Greek class, the word commonly transliterated into English as 'psyche' was said to be translatable (in the New Testament context, at least) as 'soul', 'life', or 'self'.

Also, the concept probably goes back to Plato's world of forms. A bed can be destroyed, but the idea of a bed cannot be destroyed. You can be destroyed, but your 'psyche', your soul/life/self cannot be destroyed.

So for me, it doesn't really mean as much as a lot of religion has made it out to be. As a Christian, I believe in the resurrection of the dead. For further clarification of what that means metaphysically, read whatever you can on the topic in the Bible, perhaps focusing on 1 Corinthians 15:35-54. In this particular context, Plato's focus on the perishable versus the imperishable is probably important as a point of study.