2-Step Verification is an optional security setting that requires users to enter not only their account password but also a unique code sent by Google via phone app, text message, or voice call to a previously registered device or phone number, greatly enhancing account security.
Not all devices and apps support Google's 2-Step Verification, however, and as a backup Google also allows users to generate app-specific passwords to register a unique password for that device or app. The app-specific password can be revoked at any time by logging into the user's Google account for another time, making it easy to disable access on a device that has been lost or stolen.
On OS X 10.10.2 and earlier, users setting up their machines to access Google accounts with 2-Step Verification enabled have had to use this app-specific password option. Users trying to log in with their standard Google account passwords are met with error messages informing them they need to use this option.

But as noticed by developer Jonathan Wight, the new OS X 10.10.3 beta now fully supports 2-Step Verification, allowing users to log in with their standard passwords and unique verification codes.

The change makes logging in with 2-Step protected accounts much simpler and increases security by making sure the user attempting to log in has a secondary trusted device to provide the verification code.
(Thanks, Sean!)
