Google changed their settings for Mail clients, you must Enabled the "Less secure apps" Info on enabling less secure apps: https://support.google.com/accounts/answer/6010255

Otherwise:

Two step verification  and application specific passwords:

The Google Account help advocates using two step authentication. That sends a code (a minimum of once a month but ideally every time you log in) to your cell phone that you need to enter when logging in using a browser. However applications such as email clients can't do that.

If you configure two step verification you need to create an application specific password for Thunderbird that you use instead of the normal password. The application specific password doesn't change when a new code is sent to your cell phone.

More info on setting up 2 step verification and creating the application specific pasword which you would then need to use in Thunderbird: https://support.google.com/mail/answer/1173270?hl=en

Now that I see how to get an app authentication password in Google Accounts, please tell me how to set up Thunderbird to use the 2-step authentication password.

Thunderbird does not and will never in the foreseeable future use the Google two step authentication. Nor does any other mail; program I am aware of. Perhaps because authentication is covered in the email specifications and two factor authentication is not in there to be implemented.

I keep multiple Gmail accounts in Thunderbird on a PC with Windows 8. I tried to implement Google 2-step authentication for these 3 accounts at google.com and then get Thunderbird to use it. It quickly got impossibly complicated and I couldn't understand what was happening - ie, who was asking for what password.

So, I disabled 2-step authentication at google.com. I am hoping that a strong password for the Google accounts that I change regularly gives me enough protection.

It is highly recommended to enable Google 2-step authentication. For applications not supporting 2-step authentication (such as Thunderbird) application-specific passwords must be created. https://support.google.com/accounts/answer/185833?rd=1

At the risk of repeating the information posted in the first response.

If you configure two step verification you need to create an application specific password for Thunderbird that you use instead of the normal password. The application specific password doesn't change when a new code is sent to your cell phone.

More info on setting up 2 step verification and creating the application specific password which you would then need to use in Thunderbird:

• https://support.google.com/mail/answer/1173270?hl=en

If your mail account has a remembered password, then remove those passwords, restart Thunderbird and enter the new application speicifc password. Tools > Options > Security > Passwords tab or menu icon > Options > Options > Security > Passwords tab

• click on Saved Passwords
• click on 'Show Passwords'
• select the mailbox and smtp accounts and passwords
• click on Remove
• click o close
• Click on Ok to save options.

• Close Thunderbird and wait a few moments for processes to complete.
• Restart Thunderbird

It should attempt to get mail and will prompt for the password. Then use theapplication specific password you created. Select to allow Password Manager to remember the password and click on ok.

Matt's comment is correct, Thunderbird does not use the 2 step verification, it is designed for eg: phones that access gmail, ... but if you choose to use it because you use a phone to access gmail, then Thunderbird needs the appication specific password because it cannot use the 2step verification.

All info under section : Generating application-specific passwords at the link given in the first response. https://support.google.com/mail/answer/1173270?hl=en

If you do not want nor need to use the 2 step verification method, so do noot want nor ned to creat and use the application specic spasswords then you can logon to your gmailwebmail account and enabled the "Less secure apps"