Life eternal

In 1st Timothy, one of the Pastoral Letters (a letter written by Paul to a pastor, not to a church), Paul tells his protege Timothy that those who believe in Christ receive zōēn aiōnion, or life eternal.  As a hospital chaplain and a pastor,  I have seen many terminally ill people who have not attended church for many decades turn back to their childhood faith and the comfort of the promise of a life eternal.  We look at what these ancient Greek words actually mean.  What is zōēn aiōnion?  It's not exactly what our English Bible translations would lead us to believe...