The meaning of 'owe' in this sentence is exactly what you think it is.
The situation is normally when someone's life has been saved by another. The first person had, essentially, lost their life, and the second person had given it back to him. The first person is indebted to the second for their life - they owe it to them.
In some cultures, mostly historical, this could be a literal debt - the person whose life was saved would owe the other whatever they required, up to and including sacrificing their own life for them. Nowadays the debt is not literal, but still implies that a moral debt is owed.