FeedBurner reports how many people have subscribed to your blog along with a large array of additional information about what people are reading. It also allows you to easily integrate additional features into your blog’s RSS feed, such as comment counts, and action links like “Digg This” buttons.
Darren Rowse explains the benefits in a post on this subject at ProBlogger.net:
The beauty of doing this is that now you get a fuller picture of your Feed stats. Those subscribing to your old blogger feed will now be counted in the overall Feedburner count and you’ll now be able to track what they do with your feed like you can with those who were subscribing via the Feedburner feed previously.
While Blogger users have been able to use FeedBurner all along, it wasn’t as technically easy to do so as one would like. Because of this, I often come across Blogger powered blogs where the blogger has burned their feed and put a link to their burned feed in their sidebar, yet they didn’t update the RSS URL location in their blog’s HEAD tag. Because of this, they end up splitting their subscribers between two feed URLs.
This change addresses the split issue by redirecting direct subscribers through the FeedBurner URL.