RSS (Really Simple Syndication) is a family of web feed formats used to publish frequently updated works—such as blog entries, news headlines, audio, and video. Most standard websites and blogs have a RSS or Atom feed so that the readers can get the latest update from that website straight to their Feed Reader software which can be web-based, desktop-based and mobile device-based.
For example if you'd like to subscribe to my blog's feed, just click on the orange (or blue) Feed icon on the right side of your browser's address bar. You can choose between an Atom or a RSS feed which is just 2 different feed formats but they both do basically the same thing, provide Feed syndication for your website..
Then you need to choose the software to store your feed subscription. For example, my Firefox browser gives me 3 default applications to for my feed subscription which are Bloglines, My Yahoo and Google Reader. I prefer to use Google Reader since it integrates well with my Google Account.
Click Google and select Add to Google Reader.
And that's it, my blog is added to my Google Reader feeds list. You can add practically any website/blog that you like which has a RSS or Atom feed subscription (the orange RSS icon). Even when the site or blog is blocked, you can still access the latest post from that site with your Feed Reader.
For the convenience of your readers, make sure you set your Feed Syndication to Full so that they can read the full version of your latest post and not just the snippets or summarized, text-only version. To do this on Blogger blog for example, change your Feed settings to full (see picture above).
There are literally dozens of Feed reader software ou there whether web-based, desktop-based or mobile device-based and you can always subscribe to these RSS Feeds via your web browser (such as Firefox & Internet Explorer) or your desktop e-mail client (such as Microsoft Outlook & Thunderbird). The chart above lists some of the most popular Feed readers available out there. Check out this Wikipedia link for an extensive list of all popular Feed Aggregators.