Just because a debt has been paid does not mean that it will disappear from your credit report. The main thing to understand here is that the credit report does not just reflects the things as they are on the current state but covers your credit history for a certain period of time. Different transactions and records stay on for different periods of time.
There are three main kinds of public records that are listed on a credit report.
Civil, federal and small courts judgement appear on your credit report. For example if you were sued for the amount of a certain debt and lose then that judgement will appear on your credit report and will remain there for a period of seven years from the date of filing.
Tax Liens are unpaid taxes. Unpaid taxes remain on the credit report for a period of 15 years from the reported date, while paid tax liens will stay for 7 years from the paid date.
Record of public bankruptcies remain for a period of seven to 10 years. Chapter 7 bankruptcies remain on the credit report for a period of 10 years while chapter 13 bankruptcies are deleted after seven years. Chapter 13 bankruptcies stay on for a shorter period of time as you are required to pay back at least a certain amount of debt under this kind of bankruptcy filing.
If all these three public records will find their way on your credit report and your credit report will indicate whether the debt was paid off or not. But simply paying them off will not remove them from the credit history immediately. They will stay there for the amount of time mandated by the law and regulations.
After a specified time for which the public records are meant to stay on your credit report is over they will be deleted automatically. Once they get removed from your credit report they will cease to have an impact on your credit score and you can begin to build a credit history afresh. Even during duration when the entries are being reported on your credit report the negative influence on your credit score will decrease with the passage of time. Also if tax liens and dues have been paid they would reflect the paid status in the credit report and so much the better for your credit rating.