To start off simply, feeds are a repository of data just waiting to be read. They are the best way of exchanging data between applications, and hence so widely used. Combined with a service such as FeedShake, which just appends anything new to a new feed, it can be used to chronicle your data over large timespans. If you head on there, you'll see an option to filter out data. Now, here is where things become pretty! :)
I'm going to suggest you get into the habit of converting RSS feeds to JSON if you don't get a JSON feed. It will save you loads of coding time, and make life much simpler. For that, I'll suggest Stephen's fantastic Outline Converter. Using FeedShake's service, you can create virtual categories with one feed for each category. That feed, when converted to JSON, can be used to write out data for each post! :) You can not convert it and use normal Javascript to write it out too, but thats the hard way! You can put in a category word in Braces and then have my content replacer script remove it when its written on the page. The RSS will still have the word though, and you can filter posts out that way. Have a look around and see what you can come up with!
The other thing you can do is use it to search your blog. Yes yes! You can use my Native Blog Search as well, and its more effective than this, but hey! This is just another way of doing things! Chronicle your entire blog and after converting it to JSON, just search through it using normal Javascript statements. It'll increase page-load time, but searches will be lightning fast.
Feeds find use everywhere, and you'll see it working great for you if you know how to make it work for you! This discussion continues on Bloggeratto at Feeding The Future. And while you're at it, continuing the theme of the post, why not subscribe to my feed too? You can keep a tab on whats happening! Grab it here! (The Last Word Feed)