You saved our lives, we are eternally grateful. This is what the aliens said in Tou Story when Mr. Potato Head saved them from the claw machine. They vowed there allegiance to him. In there culture, it was considered a life debt. Many cultures in the past have practiced a similar concept. Paul here in Romans is making the same kind of claim.

Romans 1:14-15 I am debtor both to the Greeks, and to the Barbarians; both to the wise, and to the unwise. So, as much as in me is, I am ready to preach the gospel...

The Apostle Paul understood what Christ had done for him. The chief of sinners himself considered the preaching of the gospel and the life lived for Christ a moral obligation. Not only an obligation but a privilege to serve Christ in whatever circumstance. Paul recognized that what Christ says was true, in this life you will have trouble but be of good cheer. Paul knew that the present sufferings of this world were nothing compared to the glory to come.

We should be as eager and willing to serve Christ no matter the cost in light of what he has done for us.

We would call this a life-debt.