This error is caused by an incorrect username or password. To change your username and / or password in Mail, take the following steps:

1. Click on the Mail menu at the top left of the screen and select Preferences
2. When the Preferences window appears, ensure the Accounts tab is selected.
3. Select the account from the left column that Connection Doctor displayed the error for.
4. Under the Account Information tab on the right, update the username and password fields halfway down the page.
5. Close the window or select another tab/account to be prompted to save your changes.
6. Re-test checking for mail and if the settings are correct there should be no problem.