Confirmation testing is also known as re-testing.
Confirmation Testing is done to make sure that the tests cases which failed in last execution are passing after the defects against those failures are fixed.
Suppose you were testing some software application and you found defects in some component.
1. You log a defect in bug tracking tool.
2. Developer will fix that defect and provide you with the official testable build.
3. You need to re-run the failed test cases to make sure that the previous failures are gone.
This is known as confirmation Testing or Re-testing