1) the first is the connection already described by David Combe. It is used to let other people know what is your account on Twitter (if you decide to make it public), and to build your Google Social Circle.
2) the second can be used to populate your Google Buzz feed with your tweets, if you are a Gmail/Buzz user. The Buzz feed is part of your Google Profile (if you like. The visibility of your Buzz feed on your Google Profile is an option, since the introduction of the new Profiles pages).
To link your tweets to your Buzz, go to
https://mail.google.com/mail/?sh..., click on the Connected sites link, and define your Twitter account as a connected site.
To make your Buzz feed visible on your Google Profile page, go to your profile (
https://profiles.google.com/me), click 'Edit profile' and use the options on the Buzz tab.