Two-factor authentication is a feature you should probably enable on any service where it's available. While Google has the handy Authenticator app, Authy improves on it in almost every way.
Two-factor authentication is a great way to keep your account a little more secure. However, using apps like Google Authenticator mean you can only access your confirmation codes via your phone (unless you intentionally set up multiple devices at first, which can be complicated). No other devices can check it. Authy syncs your authentication account to other devices so you can get the six-digit authentication code from your tablet or PC.
Perhaps the most important feature is Authy allows you to PIN-protect the app itself. If, for example, someone were to gain access to your phone or computer that had your password saved on it, there's nothing stopping someone from opening up Authenticator and entering in the authentication code. Authy ensures the user enters a four-digit PIN before they can access your two-factor tokens.
As an added bonus, Authy allows you to manage two-factor authentications from a variety of different services, including those that don't use Google Authenticator, or ones that strictly use SMS tokens. The service is a solid enhancement to two-factor authentication. Just be sure to examine your use-cases carefully. While you can sync accounts across devices, that may not be the best idea if you share a tablet or leave it unattended often.