2-factor authentication adds an extra layer of security to your account. After you enroll, instead of logging in with just your password, you'll be also asked for a code from the 2nd factor -- typically your phone, via the Authy app or and SMS text message -- before you'll be able to log in. This way, if someone steals or guesses your password they won't be able to log in to your account, as they'll still need that 2nd factor to log in.
You can enable 2-factor authentication by editing your profile in the menu in the upper right when logged in and following the directions. After you've enrolled, you can remove 2-factor authentication from the same page.
You can also optionally choose to disable SMS as an option for 2-factor authentication on this page, which increases security by blocking attacks from someone who's managed to steal your phone number (and thus can receive SMS codes from 2-factor authentication mechanisms). If you disable SMS then you must use the Authy app to provide the 2-factor authentication code. Turn off multi-device in the Authy app for the highest level of security.