Jesus drank the wine and said, "It is finished!". Then he bowed his head and gave up his spirit. (John 19:30)
"It is finished" were the last words of Lord Jesus on the cross. He had paid for all our debts of sin through his death on the cross and he has made us free from our debts.
The synonymous use of debts and sins can also be seen in the King James' version of the Lord's prayer, where we say "Forgive us our debts, as we forgive our debtors".