Whenever a change in a software application is made, it is quite possible that other areas within the application have been affected by this change. Regression testing is performed to verify that a fixed bug hasn't resulted in another functionality or business rule violation. The intent of regression testing is to ensure that a change, such as a bug fix should not result in another fault being uncovered in the application.
Regression testing is important because of the following reasons:

1: Minimize the gaps in testing when an application with changes made has to be tested.
2: Testing the new changes to verify that the changes made did not affect any other area of the application.
3: Mitigates risks when regression testing is performed on the application.
4: Test coverage is increased without compromising timelines.
5: Increase speed to market the product.