In short, it's a way to quickly and cleanly remove your data from Google Buzz, Google Contacts and Circles, Picasa, your Google Profile, and Google Stream, according to the announcement. And the Data Liberation Front is promising that support for more Google products is coming. Data is extracted in what they refer to as open file formats, so in theory, you can put your files onto competing products with no extra steps to take.
Interestingly, Google Takeout can be accessed from the Google+ (or Google Plus, if you prefer) panel, as well, indicating that part of the timing of this announcement has to do with ensuring that users know data isn't trapped within the new social network.
It's a strong step in the right direction for Google's openness policies, but I suspect that until it supports the extraction of Gmail messages and Google Docs files, most users are just going to drive right by Google Takeout.