1. Literally, owing one money. A noun or pronoun can be used between "in" and "debt." That's what loan sharks do—they get you in debt and then squeeze you dry.

2. Owing one gratitude (or, more rarely, some form of compensation, such as a favor) for their help. A noun or pronoun can be used between "in" and "debt." Helen's the one who got me a job at that great company, so I'm forever in her debt.