Basically, FeedBurner was a startup that was acquired by Google that lets you input an RSS feed, and they produce another feed. You keep the original one secret, hand out theirs, and you get analytics and other features.

Compare

http://watch.steveklabnik.com/posts.rss

to

http://feeds.feedburner.com/watch_steve_episodes

to get an idea. They called this 'burning' a feed. I guess this is what they're alluding to; give me your media file, and I'll turn that into a torrent.