pay (one's) debt
1. To repay some or all of the money one owes to someone else. A noun or pronoun can be used between "(one's) and "debt" to specify the type of debt one has accrued. I only won about $5,000 in the lottery, but it was enough to pay my credit card debt. I'm gonna be paying my student loan debt for nearly 20 years.
2. To serve the sentence given to one upon conviction of a crime. Often followed by "to society." In the eyes of the law, he has paid his debt to society, so he shouldn't be facing any further punishment for his past crimes. I spent nearly 15 years in prison—I paid my debt!
pay one's debt (to society)
Cliché to serve a sentence for a crime, usually in prison. The judge said that Mr. Simpson had to pay his debt to society. Mr. Brown paid his debt in state prison.