RSS stands for "Really Simple Syndication." Basically, it is a system that lets you receive the latest news and information from Web sites without actually having to visit those sites.
When you subscribe to an RSS feed, you can have the latest headlines and articles sent to you as soon as they are published. In the case of the Mainichi Daily News, that means getting the latest MDN articles delivered directly to you.
The first thing you'll need is a program that can receive and read RSS. This is called an "RSS reader" or "news reader." There are many different versions that can be downloaded from the Internet, as a Web search will show, and many of them are free. There are also a number of Web-based RSS readers that let you log in from any computer connected to the Internet, without having to install software.
Once you have chosen your reader, all that is left to do is subscribe to the feed you want, following the instructions of each reader. Some readers have a search function that lets you search for sources, and others let you simply cut and paste the URL of the RSS feed into the reader.
RSS readers are built into several modern browsers, and a search for "RSS reader" will provide links to other RSS software.