be in (one's) debt

1. Literally, to owe one money. That's what loan sharks do—they get you to be in their debt and then squeeze you dry. I'm worried for my life now that I'm in the mob boss's debt. Everyone in my debt pays up eventually. Even if they don't have the money at first, they always somehow, miraculously, find it in time.

2. To owe one gratitude (or, more rarely, some form of compensation, such as a favor) for their help. Helen's the one who got me a job at that great company, so I'm forever in her debt. Of course I'm in your debt—you're the one who introduced me to my wife! You saved my daughter's life. I'm forever in your debt.

be in somebody’s ˈdebt

(formal) be very grateful to somebody because they have helped you: After my divorce Ann was the only one prepared to listen to my problems, and I am forever in her debt.