A news reader (aggregator) is a stand alone app, a browser, or a 3rd party website that will check an RSS feed for updates automatically and present that content to the user when there is an update.
How It Works
Users take an RSS feed link from the blog they want to subscribe to and enter it into their news reader of choice.
The news reader is set up to check that feed for updates on timed intervals (usually every hour). This is automatic, the user doesn't have to manually check each feed. When an RSS feed has updated, the news reader can alert the user that there are new posts to be read. It is very much like your email client if you think of it that way.
Why This Is Useful
The first is most obvious. Now the user doesn't have to continually go back to the same blog only to find no new posts have been posted. Instead, the news reader acts as your alert to new posts on a blog, right as they happen.
News readers also allow multiple subscriptions. Now, instead of having to check 10 or 20 or 100 blogs each day to see if any of them have new posts, the news aggregator does this for you. You only see what's new on each blog. It saves quite a bit of time.
Types of News Readers
Two basic types of news readers are stand alone apps and browser based news readers.
Stand alone apps
Stand alone news reading apps are similar to email programs. They check for new feeds on a schedule when open, and do not when closed. They also allow a fairly great deal of flexibility because they are their own dedicated program.
However, unlike an email program, your RSS feed subscriptions are usually stored on your computer, meaning transfer of your RSS feed list and already read posts does not happen.
Browser based news readers
Browser based news readers are usually websites that work the same as a dedicated program, but allow you to do it online (similar to online email). They don't usually have as much flexibility or features as a stand alone app, but their main drawing point, like online email, is that your feed subscriptions are saved on a server, and accessable from any machine.
List of News Aggregators
http://en.wikipedia.org/wiki/List_of_news_aggregators
Who Uses News Readers?
The biggest challenge for RSS and news readers is adobption rate. I can be hard to explain to people what it is, and why it would be benefitial to use. Most people will still come to your physical website instead of opting for RSS subscriptions. However, given how easy it is to make RSS feeds (since it's built into most blogging software), having one is a must.
While it may be hard to explain to people what RSS and news readers are and do, studies have shown that a vast number of people are using RSS feeds and don't even know it.
A Nielson/Net Rating report from August 2005 shows that only 17% of people who use RSS feeds actually know that they're using them. This may be a blessing in disguise as it means the prevalance of news feed use in the public may be higher than anticipated.