My initial use case was for reading content from blogs that had been published before I'd subscribed to their feed. I could visit their site and read their previous posts, but I much prefer the slow drip of an RSS feed. So I created refeed.to to be able to add 1 post per day from the blog to my feed starting from their first post.
Since creating it I also use it to inject a few extra cartoons into my feed (xkcd every day!) and have also had fun with tech flashbacks from trustedreviews.com. So it's just a way to add a little variation to my feed.