That is part of the OAuth2 authentication process used by AOL and Yahoo. Make sure you are allowing cookies in Thunderbird, they are required.

It was working normally yesterday and today it is not Nothing has been changed ! Cookies have nothing to do with this problem. Thunderbird is not opening the accounts with the password it has already. Thunderbird is triggering a screen from yahoo and aol requiring a password and that should not be happening !!! Your answer is not valid Stan !

Cookies are required for OAuth2 authentication to stick between sessions. If those cookies are not allowed, or get cleaned out of your system, the access token that was issued during the last OAuth2 authentication process becomes invalid, so the server that issued it requires Thunderbird to authenticate again (hence a fresh prompt for login credentials). So, yes, cookies have a lot to do with this, unless we can confirm that you're not even using OAuth2. Post a screenshot of the prompt so that we know if it is in fact an OAuth2 window. Also, go to Help > Troubleshooting Information > Copy text to clipboard and paste that information here http://paste.mozilla.org/ then paste the link to it in your next reply.