Your feed is used for off-page SEO purposes too such as for providing extra reading options, RSS feed readers, aggregators, RSS email subscriptions etc.
FeedBurner just provides these features and others like email subscribing, podcasting, feedflare, buzzboost, pingshot, feedcount chicklet etc
But it just means that if you use/used Feedburner as a service that enables readers of your blog to receive your content via RSS or email every time you update the blog – that will cease working.