FeedBurner is a feed management provider that has scaled to serve 270,000 feeds and 100 million hits per day. The document discusses FeedBurner's scaling history and the solutions they implemented to address various scalability problems, including using load balancers and health checks, caching with Memcached, batch processing, partitioning tables, and implementing a disaster recovery plan using a "Panic App" to download and synchronize feeds.